Complex number - round angle

Question

$T_{\alpha}$ will be the round of the complex plane with the angle $\alpha$.

calculate - $T_{\frac{3\pi}{2}}(2-3i)$

I think it's an easy question but I'm not sure how to solve it properly

Answer 1

By definition

$$T_{\frac{3\pi}{2}}(2-3i) = (2-3i)e^{3i\pi/2}=(2-3i)(\cos(3\pi/2)+i\sin(3\pi/2)) = (2-3i)(-i)=-3-2i.$$