Question

Express the complex number in trigonometric form.

-3i

Answer 1

\(-3i\implies
\begin{array}{ccllll}
0&-3i\\
\uparrow &\uparrow \\
x&y
\end{array}\qquad
\begin{cases}
r=\sqrt{x^2+y^2}\\
\theta=tan^{-1}\left( \frac{y}{x}\right)
\end{cases}\qquad
0-3i\implies r[cos(\theta)+i\ sin(\theta)]\)

notice your "x"
notice your "y"

can you plot them both here ?

Answer 2

by plotting them, you can get the angle easy, rather than getting the tangent, which in this case will be undefined anyway

Answer 3

@jdoe0001 so would it be 3(cos 0° + i sin 0°)

Answer 4

well... what's your "r"? what's your \(\theta?\)