225. Write the purely imaginary number \( z = -3i \) in trigonometric form.
Solution. $1^{0}$. Write the given number as $z=0-3i$. Thus, $a=0, b=-3$, from which

![](https://cdn.mathpix.com/cropped/2024_05_22_db4d450c77c65a914ec1g-103.jpg?height=373&width=375&top_left_y=1427&top_left_x=120)

Fig. 12

$$
r=\sqrt{a^{2}+b^{2}}=\sqrt{0+(-3)^{2}}=\sqrt{9}=3
$$

$2^{0}$. The point corresponding to the complex number $z=-3i$ lies on the imaginary axis (Fig. 12).

$3^{0}$. The argument of this number is $3\pi / 2$, since the angle is measured from the positive direction of the $0x$ axis counterclockwise.

$4^{\circ}$. Write the given number in trigonometric form:

$$
z=3\left(\cos \frac{3 \pi}{2}+i \sin \frac{3 \pi}{2}\right)
$$

226-231. Write the complex numbers in trigonometric form: