Julia P.

asked • 03/18/15

Find all complex numbers whose sixth power equals 64

Basically, written out, looks like
(a + bi)^6 = 64

2 Answers By Expert Tutors


Mark M.

Here is another way to do this problem without DeMoivre's Theorem:
If z is a 6th root of 64, then z6 = 64.  So, z6 - 64 = 0
Factoring this as a difference of squares, we get (z3 - 8)(z+ 8) = 0
Apply the formulas for factoring a sum or difference of cubes to get:
(z - 2)(z2 + 2z + 4)(z + 2)(z2 - 2z + 4) = 0
Set each factor to 0 and solve to get the 6th roots of 64.   


Julia P.

Thank you so much! This helped me, and I was able to solve the problem correctly.


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