Equation with conjugate()



Hi

I am a newbie in maxima and I have expend some hours to understand  
what is wrong with the following: to the input

solve(z*conjugate(z)+3*(z-conjugate(z))=13+12*%i, z)

Maxima give sqrt(13+12*%i) as solution, but it is not correct!

Some suggestion?
Agust?n