# Math Help - Complex numbers - find possible values of z

1. ## Complex numbers - find possible values of z

This is my first post, so please don't kill me if I've missed something. Tried to look for a similar problem, but without any results.

"Given that the complex number z and its conjugate z* satisfy the equation zz* + iz = 66 - 8i, find the possible values for z."

The key says the answer is -8 + 2i and -8 - i.

I would be grateful for a walktrough how to calculate this (i've come a bit on the way, however I get the imaginary part to be [-1 +- srt(7)i] / 2..)

PS. sorry for the lack of latex, im in a hurry to a training, will update post later!

2. Originally Posted by mewoshh
"Given that the complex number z and its conjugate z* satisfy the equation zz* + iz = 66 - 8i, find the possible values for z."
Let $z=x+iy$.
Then $z\overline{z}+iz=x^2+y^2+ix-y=66-8i$
Now solve for $x~\&~y$.