Question

If the point represented by the complex number $iz$ is rotated about the origin through the angle $\frac{\pi }{2}$ in the counter clockwise direction then the complex number representing the new position is

• A. $iz$
• B. $-iz$
• C. $-z$
• D. $z$

Answer 1

The correct option is C $-z$

When a complex number $z$ is rotated by an angle $\theta$ in the anticlockwise direction, the resultant complex number is given by $z\times e^{i\theta }$

Similarly, here the resultant complex number is given by $\left(iz\right)\times e^{\left(i\frac{\pi }{2}\right)}=\left(iz\right)\times i=-z$