Question

Express the complex number in trigonometric form.

-4i

Answer 1

r(cos theta + i sin theta)

Answer 2

Use Euler's Identity: \(\large e^{i\theta} =\cos \theta+i\sin \theta\), where in your case \(\sin \theta =-4\) and \( \cos\theta=0\)

Answer 3

??

Answer 4

ok, thanks

Answer 5

i second that

Answer 6

r = sqrt(a^2 + b^2)
theta = tan^(-1) (b/a)

Answer 7

you need two numbers, \(r\) and \(\theta\)
\(r\) is the absolute value, which is pretty clearly \(4\) as \(-4i\) is 4 units away from the origin

Answer 8

and \(\theta\) you have a choice, but you can see the angle from the picture

Answer 9

you can use \(\theta=\frac{3\pi}{2}\) if you like or you could use \(\theta=-\frac{\pi}{2}\)