Review practice
Choose a section to work through its questions and solutions. Your progress is shared across pages. Ranges follow collection order; original source labels are kept on each question.
Section 1 · Questions 1–6
Use both conjugate constraints to determine z · Divide exactly using the conjugate of a surd denominator · +4 more
- Question 1 · Use both conjugate constraints to determine z
- Question 2 · Divide exactly using the conjugate of a surd denominator
- Question 3 · Solve coupled equations involving a conjugate
- Question 4 · Use conjugate roots and a reciprocal substitution
- Question 5 · Recover a quartic and reuse its real roots for intersections
- Question 6 · Reuse a known square after multiplying by i
Section 2 · Questions 7–12
Reuse a square root before undoing a scale and translation · Read cubic roots and rotate roots of a complex quadratic · +4 more
- Question 7 · Reuse a square root before undoing a scale and translation
- Question 8 · Read cubic roots and rotate roots of a complex quadratic
- Question 9 · Distinguish a modulus square from a complex square
- Question 10 · Evaluate a complex quadratic discriminant exactly
- Question 11 · Solve coupled equations by three algebraic methods
- Question 12 · Use a purely imaginary root to factor and transform a quartic
Section 3 · Questions 13–17
Use rotation to find area and real quadratic factors · Plot polar points and interpret a complex multiplier · +3 more
- Question 13 · Use rotation to find area and real quadratic factors
- Question 14 · Plot polar points and interpret a complex multiplier
- Question 15 · Find an exact quotient modulus without a calculator
- Question 16 · Solve a conjugate equation without assuming conjugate roots
- Question 17 · Factor a cubic and choose exact principal arguments