De Moivre's theorem~~HELP~

littlewombat

1. The problem statement, all variables and given/known data

Solve the following equations


z^3=-8i


Can anyone plz tell me how to solve this problem?

Mentallic

You can use De Moivre's theorem (actually, are you meant to?) but there is an easier way to solve it.

Notice that [tex]-8i=\left(2i\right)^3[/tex]

Apphysicist

Z=cuberoot(-8i)

So write (-8i) in r*e^(i*theta) form and then raise it to the one-third...then consider all the angles that theta could be as you round the unit circle once.

EDIT: I like Mentallic's way, haha.

Mentallic

Haha thanks