Show that the area of the triangle on the Argand diagram formed by the complex number `z ,i za n dz+i z` is `1/2|z|^2`

Explanation

we have ,` i=0 + I , 1 = cos ""pi/2 + isin pi/2 = e^((ipi)/2)`
Thus when we multiply z by I, the resulting number iz is obtained by rotating z in anticlockwise direaction through `90^(@)` about O, i.e, `triangleABC` is right angled.
AB = |z + iz -z|=|iz| = |i| |z| = |z|
AC = | z + iz- iz| = |z|
Area of ` triangle = 1/2 ( AB) (AC) = 1/2 |z|^(2)`