Question: The area of the triangle with vertices $\mathrm{A}(\mathrm{z}), \mathrm{B}(\mathrm{iz})$ and $\mathrm{C}(\mathrm{z}+\mathrm{iz})$ is :
(1) 1
(2) $\frac{1}{2}|z|^{2}$
(3) $\frac{1}{2}$
(4) $\frac{1}{2}|\mathrm{z}+\mathrm{iz}|^{2}$
Correct Option: , 3
Solution:
$A=\frac{1}{2}|z||i z|$
$=\frac{|z|^{2}}{2}$
