If z is a complex number such that z, iz and z + iz are the vertices of a triangle then

$\mathrm{A}\left(\mathrm{z}\right),\mathrm{c}\left(\mathrm{iz}\right)\text{ and }\mathrm{B}(\mathrm{z}+\mathrm{iz})$ form a right angled triangle with right angle of B.

OABC is a square of side length $\left|z\right|$

Area of triangle formed by A,B,C= $\frac{1}{2}\left(AB\right)\left(BC\right)=\frac{1}{2}\left|z\right|\left|z\right|=\frac{1}{2}{\left|z\right|}^2$

orthocentre is at the right angled vertex$\mathrm{B}(\mathrm{z}+\mathrm{iz})$

circum centre is mid point of hypotenuse =$\frac{z+iz}{2}$