Area of the triangle formed by the complex numbers z , iz and z + iz in the Argand diagram as vertices is

Step-by-step solution

Let Z=x+i y ; i z=-y+i x and Z + iz =( x - y )+ i ( x + y ) Area of triangle aligned & = 1 2 | array ccc x & y & 1 x-y & x+y & 1 -y & x & 1 array | & = 1 2 (x^2+y^2 )= 1 2 |z|^2 aligned