Not sure how to solve this trig problem dealing with the three roots of one

Solve. z to the third power -1=0

Re: Not sure how to solve this trig problem dealing with the three roots of one

$\displaystyle z^3 = 1$

z can be any of three roots of unity: $\displaystyle 1$, $\displaystyle e^{i \frac{2\pi}{3}}$, and $\displaystyle e^{i \frac{4\pi}{3}}$ (which correspond to three evenly spaced points on the unit circle).

Re: Not sure how to solve this trig problem dealing with the three roots of one

Re: Not sure how to solve this trig problem dealing with the three roots of one

Quote:

Originally Posted by

**derek1008** So is 1/2 the answer?

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Where did you get 1/2 from? Is (1/2)^3 - 1 really equal to zero?