1. The problem statement, all variables and given/known data let z' = (a,b), find z in C such that z^2 = z' 2. Relevant equations 3. The attempt at a solution let z = (x,y) then z^2 = (x^2-y^2, 2xy) since z^2 = z', we have, (x^2-y^2, 2xy) = (a,b) comparing real and imaginary components we have; x^2-y^2 = a, 2xy = b. Now, this is where i am stuck. i know i have to find z in terms of a and b. here is an attempt at what to do next; subtracting the second equation from the first, x^2 - 2xy - y^2 = a - b completing the square, (x - y)^2 - 2y^2 = a - b. ... Not asking for the answer or anything, just a push in the right direction.