Arguments determine a triangle

arg⁡z=−π/3\arg z=-\pi/3, ∣w∣=2|w|=2, arg⁡w=π/4\arg w=\pi/4 and arg⁡(w−z)=π/3\arg(w-z)=\pi/3. Let W and Z represent w,zw,z respectively.

(i) Use an Argand diagram with reference to origin O to show ∠OWZ=π/12\angle OWZ=\pi/12 radians. marks

(ii) Hence or otherwise find ∣z∣|z|. marks

[2020/DHS/Prelim/I/3 modified]

Total marks: 4

Solution

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  1. (i) Angles from directions →
  2. (ii) Sine rule →
Takeaway

Directions give angles

The argument of a difference is the direction of a side. Angles of a triangle are differences of those directions.