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The roots of the quadratic equation z^2 + bz + c = 0 are 5 + 3i and 8 - 2i.  What is b+c?

 May 10, 2024
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By Vieta's formulae we have b = -(5 + 3i + (8-2i)) = -13 - i and c = (5 + 3i)(8 - 2i) = 46 + 14i so b + c = 33 + 13i.

 May 10, 2024

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