JEE 2023 — Mathematics PYQ

Solution Summary

Numerator $i-1$ ko polar form mein badlein: $-1+i=\sqrt{2}{e}^{i\frac{3\pi }{4}}$.

Denominator pehle se polar form mein hai: $e^{i\frac{\pi }{3}}$.

$z=\frac{\sqrt{2}{e}^{i\frac{3\pi }{4}}}{e^{i\frac{\pi }{3}}}=\sqrt{2}{e}^{i(\frac{3\pi }{4}-\frac{\pi }{3})}$.

Power ko solve karein: $\frac{3\pi }{4}-\frac{\pi }{3}=\frac{9\pi -4\pi }{12}=\frac{5\pi }{12}$.

Toh $z=\sqrt{2}\left(\cos \frac{5\pi }{12}+i\sin \frac{5\pi }{12}\right)$.

• Sahi Option: (3)