JEE PYQ: Complex Numbers Question 32
Question 32 - 2019 (10 Apr Shift 2)
If $z$ and $\omega$ are two complex numbers such that $|z\omega| = 1$ and $\arg(z) - \arg(\omega) = \frac{\pi}{2}$, then:
(1) $\bar{z}\omega = i$
(2) $z\bar{\omega} = \frac{-1+i}{\sqrt{2}}$
(3) $\bar{z}\omega = -i$
(4) $z\bar{\omega} = \frac{1-i}{\sqrt{2}}$
Show Answer
Answer: (3)
Solution
$|z||\omega| = 1$, $\arg(z) = \arg(\omega) + \frac{\pi}{2}$. $\bar{z}\omega$: $|\bar{z}\omega| = |z||\omega| = 1$, $\arg(\bar{z}\omega) = -\arg(z) + \arg(\omega) = -\frac{\pi}{2}$. So $\bar{z}\omega = e^{-i\pi/2} = -i$.
BETA
