SOLUTION: Find a complex number $z$ such that the real part and imaginary part of $z$ are both integers, and such that z^2 + 2z = -53 + 8i.

Question 1209627: Find a complex number $z$ such that the real part and imaginary part of $z$ are both integers, and such that
z^2 + 2z = -53 + 8i.
Answer by mccravyedwin(408) (Show Source): You can put this solution on YOUR website!




Let z = p + qi where p and q are integers.









Set the real parts equal on both sides and set
the imaginary parts on both sides equal



Divide the second equation through by 2i



Solve the second equation for q





Substitute in




By technology, there are two solutions, neither one integers

p = -0.446924168, which gives q = 7.232281305

and

p = -1.553075832, which gives q = -7.232281305

So, there are no such integer solutions, unless somebody can 
find a mistake that I've made.

Edwin

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