Asked by Anah

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

Answers

Answered by oobleck
-4+i = √17 cis tan<sup><sup>-1</sup></sup>(-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
Answered by mathhelper
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
Answered by oobleck
??
The cube roots of −4+i
Answered by mathhelper
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.
Answered by oobleck
well, I'm sure by now @Anah will have sorted it all out ...
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