Question

Express the complex number in trigonometric form.

Answer 1

Recall the values of the trigonometric functions at the required angles:

$\begin{array}{c|c|c}\alpha&\cos(\alpha)&\sin(\alpha)\\0&1&0\\90&0&1\\180&-1&0\\270&0&-1\end{array}$

So, the number -4 can be thought of as

$-4 = 4(-1+0i) = 4(\cos(180)+i\sin(180))$