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Let \(\alpha \neq 1\) be a complex number such that the distance from \(\alpha^2\) to 1 is twice the distance from \(\alpha\) to 1, while the distance from \(\alpha^4\) to 1 is four times the distance from \(\alpha\) to 1. Find all possible values of \(\alpha\).

 Apr 3, 2019
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The possible values of alpha are 1 + i and 1 - i.

 Nov 30, 2019

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