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# The area of the triangle on the complex plane formed by the complex number $\;z \;,iz \;,$ and $\;z+iz\;$ is :

$(a)\;|z|^{2}\qquad(b)\;|\overline{z}|^{2}\qquad(c)\;\large\frac{|{z}|^{2}}{2}\qquad(d)\;None\;of\;these$

Answer : $\;\large\frac{|z|^{2}}{2}$
Explanation :
Let $\;z=x+iy\;.$ Then $\;-iz=y-ix$.
Therefore , $\;z+iz = (x-y) + i (x+y)$
Required area of the triangle $\; \large\frac{1}{2} \;(x^{2} + y^{2}) = \large\frac{|z|^{2}}{2}$