1. The problem statement, all variables and given/known data Find all solutions to z^2 + 4conjugate[z] + 4 = 0 where z is a complex number. 2. Relevant equations Alternate form: 4conjugate[z] + z^2 = -4 3. The attempt at a solution I have tried solving this solution using the quadratic formula. However, √b^2 - 4ac = √16 - 4x1x4 = 0. Therefore, as the square root is not negative, there are no imaginary numbers and the solution cannot be complex, right? Although, I am also confused with solving this, given that there is a conjugate in the equation. So, would I have to solve the equation twice, one as z^2+4z+4=0 and the other as z^2-4z+4=0? I also put the equation into wolfram alpha and got the real solution as z=-2 and the complex solutions as z=2-4i, z=2+4i. Is that the right answer? How would you get the real solution and the complex solution from the equation then?