Question

Express the complex number in trigonometric form.

-4i

Answer 1

-4i = 4(cos 270 +i sin 270)

Explanation:

We have a+ib = r(cosθ+isinθ)

`r=√(a^2+b^2)\texttt{ and }tan\theta =(b)/(a)`

Here a = 0 and b = -4

Substituting

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

-4i = 4(cos 270 +i sin 270)