Question

If the area of the triangle on the complex plane formed by the points $z,iz,z+iz$ is $200$ sq. units then $\left|z\right|$ equals

• A. $15$
• B. $10$
• C. $200$
• D. $20$

Answer 1

The correct option is D $20$

The triangle formed is an isosceles right angled triangle
Therefore it has an area
$\Rightarrow \frac{1}{2}|z{|}^2$
$=200$
$\Rightarrow |z{|}^2=400$
$\Rightarrow |z|=20$
Hence
$\Rightarrow |z|=20units.$