Show that the area of the triangle on the Argand diagram formed by the complex numbers z, zi and `z+ zi` is `=(1)/(2) |z|^(2)`

Options

A. `|z|^(2)`
B. `1/2|z|^(2)`
C. `1/4|z|^(2)`
D. `sqrt(3)/4|z|^(2)`

Answer

B

Explanation

We have `iz=ze^(ipi//2)`
This implies that iz is the vector obtained by rotating vector = in anticlockwise direction through `pi//2`. Therefore, OA `bot` AB.

`therefore` Area of `triangleOAB =1/2OA xx OB=1/2|z||iz|=1/2|z|^(2)`