Question

A number in the form a+bi is raised to the 5th power. If the answer is -3647.7-20121.9i, find the integer values of a and b.

Answer 1

I think you'll need to write -3647.7-20121.9i in polar form and then use DeMoivre's Theorem to find the five fifth roots of -3647.7 - 20121.9i.
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An approximation of the five fifth roots is given on the attached file. Based on the specification of the root you seek being integers, I would think a = -7 and b = -2.