I want to solve z^5=-1

Question

But all the examples I've seen use positive numbers. The -1 is throwing me off somewhat.

Most of the examples I've worked with would be solved using the polar form I.e

Z^5(cos5+i sin5)=1(cospi +i sinpi)

But as I said negative numbers I'm finding confusing.

Answer 1

huh? negatives are just numbers, like positives.

z^5 = -1 = 1 cisπ
z = 1^(1/5) cis(π/5)

but since cisπ = cis3π = cis5π, etc., to get all the values from 0 to 2π,

z = 1 cis(π/5 k) where k = 1,3,5,7,9

Reiny went over this with you. There are 5 5th-roots of -1. 4 of them are complex, and one of them is real: -1.

Answer 2

This question must be a popular one.

Did it yesterday

http://www.jiskha.com/display.cgi?id=1461490844