Try this beautiful problem from AIME, 2009 based on complex numbers.
There is a complex number z with imaginary part 164 and a positive integer n such that $\frac{z}{z+n}=4i$, Find n.
Complex Numbers
Theory of equations
Polynomials
Answer: 697.
AIME, 2009, Problem 2
Complex Numbers from A to Z by Titu Andreescue .
Taking z=a+bi
then a+bi=(z+n)4i=-4b+4i(a+n),gives a=-4b b=4(a+n)=4(n-4b)
then n=$\frac{b}{4}+4b=\frac{164}{4}+4.164=697$
