There are six different sixth roots of 64. that is, there are six complex numbers that solve x^6=64

There are two possible solutions:

1)
When we know that:



when

then:



For we have:



and:



k = 0



k = 1



k = 2



k = 3



k = 4



k = 5



So the answer is:



2)
We don't know method (1). If so, we could use following identities:



There will be:



Now, we complete the square for:



and for:



When we return to :



And we have

Iknow one of the answers is a and maybe b but not 100% sure about b