Question

Express the complex number in trigonometric form. -4i

Answer 1

Answer:

-4i =  4(cos 270 +i sin 270)

Step-by-step explanation:

We have a+ib = r(cosθ+isinθ)

$r=\sqrt{a^2+b^2}\texttt{ and }tan\theta =\frac{b}{a}$

Here a = 0  and b = -4

Substituting

       $r=\sqrt{0^2+(-4)^2}\\\\r=4\\\\tan\theta =\frac{-4}{0}\\\\\theta =270^0\texttt{(Since a is zero and b is negative)}$

-4i =  4(cos 270 +i sin 270)