Question

Express the complex number in trigonometric form.

-2i

Answer 1

\(\large {
-2i\implies 0-2i\implies
\begin{array}{cccllll}
(0&,&-2)\\
x&&y
\end{array}\qquad r=\sqrt{x^2+y^2}\qquad (r,\theta)
}\)

Answer 2

\[z = a+bi = r (\cos \theta +i \sin \theta)\]
\[a^2 + b^2 = r^2\]
\[\frac{b}{a} = \tan \theta\]

for this problem:
a = 0
b = -2

Answer 3

now if you graph ( 0, -2) where would you end up as an angle \(\theta?\)

Answer 4

Is it 270 degrees?

Answer 5

yeap