Question

If z ≠ 0 is a complex number, then z, iz, -z and - iz are the vertices of a 

(1) Square 

(2) rectangle 

(3) rhombus 

(4) all of these 

Answer 1

Correct option is (4) all of these 

Let z,iz,- z and - iz are represented by A, B, C and D in the complex plane. We have

Midpoint of AC = {z + ( - z)}/ 2 =0 and midpoint of BD= {iz + (- iz)}/ 2 = 0 

Thus the diagonals bisect each other.

Also AC = |- z - z| = 2|z|.

And BD = |- iz - iz| = 2|z|. AC = BD

AB = |iz - z| = |i - 1||z| = √2|z|

BC = |- iz - z|= |-i -1||z| = √2|z|