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# Complex Numbers

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Let $$z$$ be a complex number such that $$z^5 + z^4 + 2z^3 + z^2 + z = 0$$
Find all possible values of $$|z|$$

List all possible values, separated by commas.

Sep 2, 2021

#1
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The equation factors as z(z^2 + z + 1)^2 = 0, so the solutions are $0, -\frac{1}{2} + \frac{\sqrt{3}}{2} i, -\frac{1}{2} - \frac{\sqrt{3}}{2} i$.

Sep 2, 2021
#2
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Feedmepi.

If you do not like an answer you are best to comment. (A proper informative comment)

Just taking points off will not let other people know that you are unhappy with the answer.

Sep 9, 2021
edited by Melody  Sep 9, 2021