Question

If z = x + i y, then the area of the triangle whose vertices are points z, iz and z + iz is

• A.
• B. 2
• C.
• D.

Answer 1

The correct option is A

BC = AD = $\left|z\right|$

CD = AB = $\left|z\right|$

We want to find the area of the triangle ABD. It is a right-angled triangle wid A = ${90}^{\circ }$

$\Rightarrow$ Area = $\frac{1}{2}$ $\times$ AB $\times$ AD

= $\frac{1}{2}$ $\left|z\right|$ $\times$ $\left|z\right|$

= $\frac{1}{2}$ $|z{|}^2$