## itsrainingmacey 3 years ago how would i find the 5th roots of -2i? (leave the answers in polar form and the angle in degrees) thank you!

1. KingGeorge

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

2. itsrainingmacey

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

3. KingGeorge

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$\Large 2e^{\frac{3i\pi}{2}}$

4. itsrainingmacey

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

5. KingGeorge

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

6. itsrainingmacey

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

7. KingGeorge

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