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I have the following question,Find the complex numbers u=x+y such that x and y are all real numbers and $u^2=−15+8i$

What I am thinking to do is solve for u but that doesnt seem right, I am also thinking that since u is stated and it ask for $u^2$ I am thinking of doing $(-15+8i)(-15+81)$ and solve from there but still not sure if thats the right direction.

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  • $\begingroup$ Does "complex square roots" ring a bell? $\endgroup$ Commented Oct 31, 2016 at 17:37
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    $\begingroup$ Surely you mean $u=x+yi$, not $u=x+y$. $\endgroup$ Commented Oct 31, 2016 at 17:47
  • $\begingroup$ Not to pile it on, but two real numbers add up to a real number, and that real number squares to another real number. Like @Théophile said, it looks like you meant $u = x + yi$. $\endgroup$ Commented Oct 31, 2016 at 20:48

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One possible way: Let $u = a+bi$, with $a$ and $b$ real. Calculate $(a+bi)^2$, equate that to $-15 + 8i$, and solve the system of equations you get, with $a$ and $b$ as the unknowns.

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