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There exists a complex number of the form $z = x + yi,$ where $x$ and $y$ are positive integers, such that \[z^3 = -74 + ci,\]for some integer $c.$ Find $z.$

 Sep 30, 2020
 #1
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c = 84.

 Sep 30, 2020
 #2
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\(\displaystyle (1+5i)^{3}=-74-110i.\)

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 Oct 1, 2020

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