Find the fifth roots of 32(cos 280° + i sin 280°

I know i need to use DeMoivre's theorem but i need a refresher on how to do the process, I know that at some point all you do is add a certain amount into the equation too.

Question

Find the fifth roots of 32(cos 280° + i sin 280°

I know i need to use DeMoivre's theorem but i need a refresher on how to do the process, I know that at some point all you do is add a certain amount into the equation too.

anonymous · Answer

What is the DeMoivre's theorem? Can you state it out?

anonymous · Answer

@e.mccormick  @hartnn

anonymous · Answer

@amistre64

anonymous · Answer

@ganeshie8

amistre64 · Answer

http://www.mathwords.com/d/demoivres_thm.htm

anonymous · Answer

Thank you do you know if I would make the 32 into 2^5
?

amistre64 · Answer

that might be useful yes

[32(cos 280° + i sin 280°)]^(1/5)

2(cos 280/5° + i sin 280/5°)

anonymous · Answer

And don't I add 360 to the angles? or do i also have to divide 360 by 5 for 72?

amistre64 · Answer

you can do $$\frac{\theta+360k}{n}$$yes

anonymous · Answer

where k are the roots, 0, 1, 2, 3, 4?
What would n be?

anonymous · Answer

5?

amistre64 · Answer

n = 5 ...

anonymous · Answer

okay, sorry,

amistre64 · Answer

a fifth root is when the exponent is 1/5  so the angle is multiplied by the 1/5 ... or simply a divide by 5 in this case

anonymous · Answer

The theta would be 280, or after dividing my 5, 56, correct?

amistre64 · Answer

360/5 = 72

so the angles are going to start at 280 and increase/decrease by 72  is anothe rway to look at it

anonymous · Answer

okay, thank you very much @amistre64

amistre64 · Answer

your welcome