Question

Area of the triangle in the argand diagram formed by the complex numbers $z,iz,z+iz$, where $z=x+iy$ is

• A. $|z|$
• B. $|z{|}^2$
• C. $2|z{|}^2$
• D. $\frac{1}{2}|z{|}^2$

Answer 1

Answer: (D)

since, $iz=z{e}^{i\frac{\pi }{2}}$
This implies that $iz$ is the vector obtained by rotating vector $z$ in anticlock wise direction through $90^{\circ }$
$\therefore OA\perp AB$

So, area of $\Delta OAB=\frac{1}{2}OA\times OB$
$=\frac{1}{2}|z||iz|=\frac{1}{2}|z{|}^2$