Math Help - Complex Numbers

1. Complex Numbers

Hi guys, need help with this question:

Find the 2 complex numbers z1 and z2 each of which satisfies the following EQN:

3zz* + 2(z-z*) = 39 + 12i

To solve this, I let z = x + yi
3zz* + 2(z-z*) = 39 + 12i
=> 3(x^2 + y^2) + 2y = 39 + 12i

Equating Real and Imaginary parts:
3x^2 = 39 => x = sq root 13
3y^2 + 2y = 12 => y = (-1/3) + sq root (37/9)

However, my ans was wrong. Any idea what went wrong? Thanks in advance!

2. Assuming that you're using z* to represent $\displaystyle \overline{z}$, you should note that $\displaystyle 2(z - \overline{z}) = 2[x+iy - (x-iy)] = 2(2iy) = 4iy$.

Fix the rest.

3. _ _
3ZZ = 3(x^2+y^2) and 2(z-z) =4iy
therefore equating real and imaginary parts we get

3(x^2+y^2) = 39 and 4y = 12

y = 3 gives x = +2 & -2