234. Write the number $z=-5 i$ in trigonometric and exponential forms.
Solution. To represent the number $z$ in the form $z=r(\cos \varphi+$ $+i \sin \varphi$ ) and $z=r e^{i \varphi}$, we need to find the modulus and argument of the number $z$. Here $a=$ $=0, b=-5$; then $r=\sqrt{0+(-5)^{2}}=5$; $\varphi=3 \pi / 2$, since the point $z$ lies on the imaginary axis of the complex plane. Knowing $r$ and $\varphi$, we get $z=5\left(\cos \frac{3 \pi}{2}+i \sin \frac{3 \pi}{2}\right)$ and $z=$ $=5 e^{\frac{3 \pi}{2} i}$.