how would i find the 5th roots of -2i? (leave the answers in polar form and the angle in degrees)

thank you!

Question

how would i find the 5th roots of -2i? (leave the answers in polar form and the angle in degrees)

thank you!

kinggeorge · Answer

First, you need to change -2i into polar form. Can you show me what you get when it's in polar form?

anonymous · Answer

Is it 2cis0? I'm not entirely sure.

kinggeorge · Answer

On a graph, |dw:1353369315067:dw|-2i is located there. The angle from the positive real axis, to the negative imaginary axis, is $3\pi/2$. So the polar form should be $$2\text{ cis} (3\pi/2)$$or$$\Large 2e^{\frac{3i\pi}{2}}$$

anonymous · Answer

Oh! Okay, I see! I'm going to work it out with the information you have just given me. Thank you!

kinggeorge · Answer

As a hint, it's a lot easier to take roots of $2e^{\frac{3i\pi}{2}}$

anonymous · Answer

So far, I have 2cis3pi/10 and 2cis7pi/10.

Am I on the right track?

kinggeorge · Answer

Remember that you need to have $$\Large \sqrt[5]{2}$$out in front of those, but otherwise, I think those are correct.