Let a complex number be w=1-sqrt(3) i . Let another complex number z be such that |zw|=1 and arg(z)-arg(w)=(pi)/(2) . Then the area of the triangle with vertices origin, z and w is equal to :

Complex Numbers: Let a complex number be w=1-sqrt(3) i . Let another complex number z… | JEE Main 2021

JEE Main 2021 (Online) 18th March Evening ShiftQuestion 1

Let a complex number be $w=1-\sqrt{3}\,i$. Let another complex number $z$ be such that $|zw|=1$ and $\arg(z)-\arg(w)=\frac{\pi}{2}$. Then the area of the triangle with vertices origin, $z$ and $w$ is equal to :

Complex Numbers

$\frac{1}{2}$✓ Correct answer$2$$\frac{1}{4}$$4$

Solution

$|w|=2$, $\arg w=-\pi/3$. $|z|=\frac12$, $\arg z=\arg w+\frac\pi2$, so $z\perp w$. Area $=\frac12\cdot2\cdot\frac12=\frac12$. Option (A).

Complex Numbers - JEE Mathematics question (JEE Main 2021 (Online) 18th March Evening Shift)

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