Question

If O is origin and affixes of P, Q, R are respectively $z,iz,z+iz$. Locate the points on complex plane. If $\Delta PQR=200$, then $|z|$ is

• A. 10
• B. 30
• C. 20
• D. 100

Answer 1

The correct option is C 20

$P=z,Q=iz$ and $R=z+iz$

$\Rightarrow △PQR=200,$ $\left|z\right|=?$

$\Rightarrow \overrightarrow{RP}=\overrightarrow{z}$

$\overrightarrow{PQ}=\overrightarrow{iz}$

$\overrightarrow{RQ}=z+iz$

$\Rightarrow$ Area of $△RPQ=|\frac{1}{2}\times PR\times PQ|$

$\Rightarrow 200=|\frac{1}{2}\times z\times iz|$

$\Rightarrow 200=\frac{{\left|z\right|}^2}{2}$

$\Rightarrow \left|z\right|=\sqrt{400}=20$

Hence, the answer is $20.$