Question

The complex number $z=1+i$ represented by the point $P$ in argand plane and $OP$ is rotated by an angle of $\frac{\pi }{2}$ in counter clock wise direction then the resulting complex number is

• A. $\overline{z}$
• B. z
• C. $-\overline{z}$
• D. $\frac{\overline{z}}{|z{|}^2}$

Answer 1

The correct option is C $-\overline{z}$

$z=1+i$
$\therefore argz={\tan }^{-1}\left(\frac{1}{1}\right)$ $=\frac{\pi }{4}$
Let the complex number obtained after rotation be $z_1$
$\therefore arg\left(z_1\right)=\frac{\pi }{4}+\frac{\pi }{2}$
$=\frac{3\pi }{4}$
$z_1=-1+i$

Now,

$\overline{z}=1-i$

Hence, $z_1=-\overline{z}$