It is obvious that is a solution.
The angle of -8 is since it lies on the negative x axis.
Where k goes from 0 to 1 less than the n so k = 0, 1, 2 and n = 3.
Principle root:
Hi,
I was reading a textbook when I came upon their discussion on De Moivre's Theorem. The book talked about the difference between and , and they said something about how De Moivre's Theorem let us conclude that there are 3 cube roots of a number and 6 sixth roots. Can anyone decipher what this means?
Thanks!
-Masoug
-8 has one real cube root (-2 as dwsmith says) and two complex roots. -8 has six complex (non-real) roots but if you square those, you will find that there are three sets of pairs that have the same square-giving you again the 3 cube roots of -8. For example, two of the sixth roots of -8 are and both of which have square equal to -2.