Question

A Complex number $Z$ is multiplied $by-1$, then $Z$ is rotated through an angle of

• A. $\pi$ in clockwise direction
• B. $\pi$ in anti clock direction
• C. $\frac{\pi }{2}$ in anti clock direction
• D. $\frac{\pi }{2}$ in clockwise direction

Answer 1

The correct option is B $\pi$ in anti clock direction

When $z$ is multiplied by $-1$, it changes to $-z$

$⟹z$ changes to $z{e}^{i\pi }$ ....... $(\because e^{i\pi }=\cos \pi +i\sin \pi =-1)$
$⟹z$ is rotated through $\pi$ in anti-clockwise direction.
Hence, option B is correct.