Right, this comes in 2 parts, the 1st part is that this problem is part (b) of a question, in part (a) you are given z= 3+5i however i don't know if you can/need to use this fact for this part of the question (gotta love my teachers ). second part is the question itself:

Solve the equation z^2 + 2z*= -3, where z* denotes the complex conjugate of z.

thanks in advance for any help, really appreciate it.