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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 + 14 = -74 + ci,

for some integer c.  Find z.

 Jun 11, 2021
 #1
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z^3-ci = -88 so that means that the imaginary part of z^3 is c and than the real part of z^3 is -88. So, x^3-3xy^2 = -88 so x=2,y=4 which means z=2+4i

 Jun 12, 2021

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