Question

Let the point P represent the complex number z. If OP is turned round O by an angle $\frac{\pi }{2}$ in the clockwise sense where O is the origin then in the new position of P represents the complex number .................

• A. - z
• B. - iz
• C. z
• D. iz

Answer 1

The correct option is B - iz

Rotation due to anticlockwise is positive and in clockwise sense is negative.
Hence
Let
$z=e^{i\theta }$
$=cos\theta +isin\theta$
Now if we rotate it by $\frac{\pi }{2}$ in clockwise sense , we get
$cos(\theta -\frac{\pi }{2})+isin(\theta -\frac{\pi }{2})$
$=sin\theta -icos\theta$
$=-i(isin\theta +cos\theta )$
$=-i(cos\theta +isin\theta )$
$=-iz$