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

Question

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