
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(zz*) = 39 + 12i
To solve this, I let z = x + yi
3zz* + 2(zz*) = 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! (Happy)

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

_ _
3ZZ = 3(x^2+y^2) and 2(zz) =4iy
therefore equating real and imaginary parts we get
3(x^2+y^2) = 39 and 4y = 12
y = 3 gives x = +2 & 2