PorismaSource review

Your source-to-article checklist

Source review · Complex numbers

All source-review topics · Coverage and provenance · Student practice

Every question has a place in the ledger. That does not prove every item is accurate or complete. Use these links to compare the native question, subparts, working, teaching notes, tables and diagrams with your private originals.

“Source comparison recorded” means a visual source-comparison pass is documented. “Mapped” or “generated” describes an ingestion step. Mathematical review, browser interaction tests and settled screenshot review are separate checks.

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19 question records

Optional ticks record your own inspection in this browser only. They do not change the conversion or mathematical-review claims.

15 · Complex numbers

Edition metadata →

15-01 · Eliminate with complex coefficientsQuestion pp.1 / Solution pp.1

Question and explanations → · Complete native source article →

[2017/MJC/Prelim/I/3]. Printed/task labels inventoried: main.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

1 page-item record.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

Essential answer conditions and source qualifications

No separate condition recorded. Check the full question, native working and printed assumptions.

Exact private source page references

15 complex numbers.pdf · p.1
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.1

15-02 · Reduce a complex system to a quadraticQuestion pp.1 / Solution pp.1, 2

Question and explanations → · Complete native source article →

[2024/ACJC/Prelim/I/1]. Printed/task labels inventoried: main.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Teacher notes

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

Essential answer conditions and source qualifications

No separate condition recorded. Check the full question, native working and printed assumptions.

Exact private source page references

15 complex numbers.pdf · p.1
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.1
15 complex numbers sol.pdf · p.2

15-03 · Conjugation and component equationsQuestion pp.1 / Solution pp.2, 3

Question and explanations → · Complete native source article →

[2015/JJC/Prelim/II/1]. Printed/task labels inventoried: a.i, a.ii, b.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

3 page-item records.

Inspect native target → I compared this with the original

Teacher notes

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

1 page-item record. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

Essential answer conditions and source qualifications

No separate condition recorded. Check the full question, native working and printed assumptions.

Exact private source page references

15 complex numbers.pdf · p.1
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.2
15 complex numbers sol.pdf · p.3

15-04 · Arguments after rotation and reflectionQuestion pp.1 / Solution pp.3

Question and explanations → · Complete native source article →

[modified 2023/HCI/Prelim/II/3a]. Printed/task labels inventoried: i, ii.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Teacher notes

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

1 page-item record. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

An inverse tangent alone does not identify the quadrant.

Essential answer conditions and source qualifications

Principal arguments in (−π,π].

Exact private source page references

15 complex numbers.pdf · p.1
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.3

15-05 · Square roots followed by a quadratic shiftQuestion pp.1 / Solution pp.4

Question and explanations → · Complete native source article →

[2024/RVHS/Prelim/I/5b]. Printed/task labels inventoried: i, ii.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Teacher notes

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

Essential answer conditions and source qualifications

No separate condition recorded. Check the full question, native working and printed assumptions.

Exact private source page references

15 complex numbers.pdf · p.1
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.4

15-06 · A modulus equation imposes a signQuestion pp.1 / Solution pp.5, 6

Question and explanations → · Complete native source article →

[2023/CJC/Prelim/I/1]. Printed/task labels inventoried: main.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

3 page-item records.

Inspect native target → I compared this with the original

Teacher notes

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

The printed first equation contains modulus bars; plain extraction omits them. Squaring creates a rejected candidate.

Essential answer conditions and source qualifications

main

The squared-equation candidate a=−19/15 violates 4 a−7≥0.

Exact private source page references

15 complex numbers.pdf · p.1
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.5
15 complex numbers sol.pdf · p.6

15-07 · Root midpoint and a parallelogramQuestion pp.2 / Solution pp.7, 8

Question and explanations → · Complete native source article →

[2022/VJC/Promo/9]. Printed/task labels inventoried: i, ii, iii, iv.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

3 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

1 page-item record.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

1 page-item record. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

Essential answer conditions and source qualifications

No separate condition recorded. Check the full question, native working and printed assumptions.

Exact private source page references

15 complex numbers.pdf · p.2
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.7
15 complex numbers sol.pdf · p.8

15-08 · Conjugate roots and transformed equationsQuestion pp.2 / Solution pp.8, 9

Question and explanations → · Complete native source article →

[2023/CJC/Prelim/I/4 modified]. Printed/task labels inventoried: a, b, c, d.i, d.ii.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Teacher notes

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

2 page-item records. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

Essential answer conditions and source qualifications

No separate condition recorded. Check the full question, native working and printed assumptions.

Exact private source page references

15 complex numbers.pdf · p.2
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.8
15 complex numbers sol.pdf · p.9

15-09 · A cubic discriminates real from complex rootsQuestion pp.2 / Solution pp.10, 11

Question and explanations → · Complete native source article →

[2020/VJC/Prelim/I/5]. Printed/task labels inventoried: i, ii, iii.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

3 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

1 page-item record.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

1 page-item record. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

Three distinct real roots require strict inequalities; “only real roots” includes repeated roots.

Essential answer conditions and source qualifications

iii

Repeated roots allowed; three distinct real roots require −2<c<2.

Exact private source page references

15 complex numbers.pdf · p.2
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.10
15 complex numbers sol.pdf · p.11

15-10 · Use conjugacy only with real coefficientsQuestion pp.3 / Solution pp.11, 12, 13

Question and explanations → · Complete native source article →

[2017/IJC/Prelim/I/4]. Printed/task labels inventoried: a, b.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

3 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

The conjugate of a root need not be a root of a polynomial with complex coefficients.

Essential answer conditions and source qualifications

No separate condition recorded. Check the full question, native working and printed assumptions.

Exact private source page references

15 complex numbers.pdf · p.3
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.11
15 complex numbers sol.pdf · p.12
15 complex numbers sol.pdf · p.13

15-11 · A purely imaginary root unlocks a cubicQuestion pp.3 / Solution pp.13, 14

Question and explanations → · Complete native source article →

[2018/RI/Promo/11a]. Printed/task labels inventoried: i, ii.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

3 page-item records.

Inspect native target → I compared this with the original

Teacher notes

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

Essential answer conditions and source qualifications

No separate condition recorded. Check the full question, native working and printed assumptions.

Exact private source page references

15 complex numbers.pdf · p.3
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.13
15 complex numbers sol.pdf · p.14

15-12 · Factor a real quartic by a conjugate pairQuestion pp.3 / Solution pp.14, 15, 16

Question and explanations → · Complete native source article →

[2024/YIJC/Prelim/I/3]. Printed/task labels inventoried: a, b.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

4 page-item records.

Inspect native target → I compared this with the original

Teacher notes

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

Essential answer conditions and source qualifications

No separate condition recorded. Check the full question, native working and printed assumptions.

Exact private source page references

15 complex numbers.pdf · p.3
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.14
15 complex numbers sol.pdf · p.15
15 complex numbers sol.pdf · p.16

15-13 · Quartic roots and an Argand triangleQuestion pp.3 / Solution pp.17

Question and explanations → · Complete native source article →

[2024/DHS/Prelim/I/7]. Printed/task labels inventoried: a, b, c.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Teacher notes

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

1 page-item record. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed with source qualification; see warning and topic review evidence. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

The printed polynomial assumes a monic quartic; the literal root data permit any nonzero real scalar multiple.

Essential answer conditions and source qualifications

Printed K=1 assumes an unstated monic polynomial.

Exact private source page references

15 complex numbers.pdf · p.3
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.17

15-14 · Five points from one polar vectorQuestion pp.3 / Solution pp.18

Question and explanations → · Complete native source article →

[modified 2019/NJC/Prelim/I/1]. Printed/task labels inventoried: main.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

1 page-item record.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

1 page-item record.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

1 page-item record. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

Essential answer conditions and source qualifications

main

$0<r<1$ , $\pi/2<\theta<\pi$ ; plot represents this family.

Exact private source page references

15 complex numbers.pdf · p.3
15 complex numbers sol.pdf · p.18

15-15 · A real conjugate sum has two directionsQuestion pp.4 / Solution pp.18

Question and explanations → · Complete native source article →

[2020/VJC/Prelim/II/3a]. Printed/task labels inventoried: main.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

1 page-item record.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

1 page-item record. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

Essential answer conditions and source qualifications

No separate condition recorded. Check the full question, native working and printed assumptions.

Exact private source page references

15 complex numbers.pdf · p.4
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.18

15-16 · Find a square using a quarter-turnQuestion pp.4 / Solution pp.19

Question and explanations → · Complete native source article →

[2016/VJC/Prelim/II/3]. Printed/task labels inventoried: main.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

1 page-item record.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

1 page-item record. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

Essential answer conditions and source qualifications

No separate condition recorded. Check the full question, native working and printed assumptions.

Exact private source page references

15 complex numbers.pdf · p.4
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.19

15-17 · Arguments determine a triangleQuestion pp.4 / Solution pp.19, 20

Question and explanations → · Complete native source article →

[2020/DHS/Prelim/I/3 modified]. Printed/task labels inventoried: i, ii.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Teacher notes

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

1 page-item record. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

The angle of w−z belongs to the vector ZW, not WZ.

Essential answer conditions and source qualifications

No separate condition recorded. Check the full question, native working and printed assumptions.

Exact private source page references

15 complex numbers.pdf · p.4
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.19
15 complex numbers sol.pdf · p.20

15-18 · A complex square gives an exact tangentQuestion pp.4 / Solution pp.20, 21

Question and explanations → · Complete native source article →

[2010/MJC/Prelim/I/11]. Printed/task labels inventoried: shape, identity.

Question / subparts

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Solution steps

Source comparison recorded

2 page-item records.

Inspect native target → I compared this with the original

Teacher notes

Source comparison recorded

1 page-item record.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

Inspect native target → I compared this with the original

Diagrams

Source comparison recorded

1 page-item record. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

Essential answer conditions and source qualifications

No separate condition recorded. Check the full question, native working and printed assumptions.

Exact private source page references

15 complex numbers.pdf · p.4
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.20
15 complex numbers sol.pdf · p.21

15-19 · Complex division yields an exact sineQuestion pp.4 / Solution pp.22, 23

Question and explanations → · Complete native source article →

[modified 2013/TJC/Prelim/I/5]. Printed/task labels inventoried: i, ii, iii.

Question / subparts

Source comparison recorded

2 page-item records.

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Solution steps

Source comparison recorded

3 page-item records.

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Teacher notes

Source comparison recorded

1 page-item record.

Inspect native target → I compared this with the original

Tables

No item inventoried — owner check needed

0 page-item records.

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Diagrams

Source comparison recorded

2 page-item records. Native SVG generated; rendering is checked separately

Inspect native target → I compared this with the original

Short answer: source-compared
Mathematical correctness: reviewed: independently derived and compared with rendered question/answer pages. Recorded mathematical review is a first pass; it is not independent expert certification.
Final interactions: Question-first question/short-answer pixels reviewed at320px on baseline9f03a4f. This polish pass adds all248 open-guided DOM reflow checks; all31 added given-figure placements inspected at320px; responsive plots and selected updated layouts checked separately. This is not an exhaustive new working/teacher-note pixel audit.
Rendered source content: Settled source-content screenshots reviewed

Argument subtraction may need reduction into the principal interval; here −11π/12 already lies there.

Essential answer conditions and source qualifications

No separate condition recorded. Check the full question, native working and printed assumptions.

Exact private source page references

15 complex numbers.pdf · p.4
15 complex numbers.pdf · p.5
15 complex numbers sol.pdf · p.22
15 complex numbers sol.pdf · p.23

An empty omission list is not a completeness certificate. Add any issue you find to the article or page-item record before calling that part finished.