SOLUTION: If 1 and w are 2 of the 5 roots of (w)^5 = 1, then prove the following: a) (w)^2, (w)^3, and (w)^4 are the remaining roots of (w)^5 = 1 b) 1 + w + (w)^2 + (w)^3 + (w)^4 = 0

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Question 1181163: If 1 and w are 2 of the 5 roots of (w)^5 = 1, then prove the following:
a) (w)^2, (w)^3, and (w)^4 are the remaining roots of (w)^5 = 1
b) 1 + w + (w)^2 + (w)^3 + (w)^4 = 0
c) (w)^(5n) = 1 for any integer n
Found 2 solutions by Edwin McCravy, mccravyedwin:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
If 1 and w are 2 of the 5 roots of (w)^5 = 1, then prove the following:
a) (w)^2, (w)^3, and (w)^4 are the remaining roots of (w)^5 = 1
where cis(θ) = cos(θ)+isin(θ),
The 5 fifth roots of 1 are
b) 1 + w + (w)^2 + (w)^3 + (w)^4 = 0, provided w ≠ 1



Since w ≠ 1, w-1 ≠ 0, so
c) (w)^5n = 1 for any integer n

Raise both sides to the 5th power:



Edwin
Answer by mccravyedwin(407)   (Show Source): You can put this solution on YOUR website!

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