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
The cube roots of −4+i
Answers
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
so the 4th roots are
1.60352 cis 2.8966/3 = 1.60352 cis 0.9655 + k * 2π/3
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
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
oobleck
??
The cube roots of −4+i
The cube roots of −4+i
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.
Sorry about the confusion.
oobleck
well, I'm sure by now @Anah will have sorted it all out ...