1. The problem statement, all variables and given/known data For z = x+iy find the relationship between x and y so that (Imz2) / z2 = -i 2. The attempt at a solution I attempted this in a few different ways (i.e. looking at the exponential and trig forms of complex numbers)... I settled on simple FOIL which gave me the following: (x+iy)^2 = x^2 + i2xy - y^2 The imaginary part is 2xy; so: 2xy / (x^2 + i2xy - y^2) = -i <-- from original problem from here, multiplying -i by the denominator gives: 2xy = -ix^2 + 2xy + iy^2 Cancel out 2xy to get zero on the left side, and factor out i, leaving: x^2 = y^2 However.... this does not seem to produce any solutions resulting in -i. For example, if x=2 and y=2, z^2 = 8i ... for x=-2 and y=2, z^2 = -8i ... The problem is, there never seems to be a sign change for Im(z^2) over z^2. Is this problem flawed, or am I missing something obvious...?