Question 1183762: (a) Find the sixth roots of 1.
(b) Find the fifth roots of 32. Found 2 solutions by Boreal, greenestamps:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! the first ia -1 and 1 if you want the sixth root. If you want the six rootS, they are -1 with multiplicity 3 and 1 with multiplicity 3. I think you want -1, 1 with this question, but the wording matters.
the second is 2.
The answer from the other tutor is incomplete/incorrect. There are 6 6th roots of 1 (or any other number); there are 5 5th roots of 32 (or any other number). The response from the other tutor only shows the real roots -- 2 of the 6 6th roots of 1, and 1 of the 5 5th roots of 32.
De Moivre's Theorem solves this kind of problem easily.
Given a number represented in trigonometric form
or ,
de Moivre's Theorem says that the "primary" n-th root is
and the other n-th roots have the same magnitude as the primary root and are distributed around the Argand plane at intervals of
(a) The 6 6th roots of 1
The primary root is
The other 6th roots of 1 are distributed about the Argand plane at intervals of ; so the 6 6th roots of 1 are
