Question

Find the indicated roots of the following. Express your answer in the form found using Euler's Formula, |z|neinθ.

The cube roots of −4+i

Answer 1

-4+i = √17 cis tan^{^-1}(-1/4) = 4.1231 cis 2.8966
so the 4th roots are
1.60352 cis 2.8966/3 = 1.60352 cis 0.9655 + k * 2π/3

Answer 2

I got

z^(1/4) = (√17)^(1/4) cis (2.8966/4)

primary root = 1.425 cis .7242

general solution:
1.425 cis (.7242 + k*π/2) where k = 0,1,2,3
(you are dividing 2π into 4 parts , not 3
you have to take the 4th root of √17, you took the third)

in degrees
1.425 cis (41.49° + k(90) ), for k = 0,1,2,3

Answer 3

??
The cube roots of −4+i

Answer 4

I think I should have read the original question except the second line of your answer, where you are talking about the fourth root.

Sorry about the confusion.

Answer 5

well, I'm sure by now @Anah will have sorted it all out ...