Porisma

A hint to get started

Plot polar points and interpret a complex multiplier

The numbers z1,z2z_1,z_2 satisfy ∣z1∣=4|z_1|=4, arg⁡z1=π/3\arg z_1=\pi/3, ∣z2∣=2|z_2|=2, arg⁡z2=−π/6\arg z_2=-\pi/6.

(i) On an Argand diagram with origin OO, mark their points and deduce the exact value of ∣z1−z2∣|z_1-z_2|. marks

(ii) Write down a number aa such that z1=az2z_1=az_2. Hence or otherwise describe their geometric relationship. marks

[2023/RVHS/II/1(modified)]

CJC · Review problems · Question 14

Subtract the directed arguments to obtain the angle between rays.

Read the worked solution