Finding complex solutions from an eqn.

[JC3187]

Given z = 1 + i,

Find all complex solutions to z^{2} + Conjugate:z^{2} = 0

I have come up with a way to solving this but it doesn't make any sense.

would it be:
z^{2} + 1-i = 0

z^{2} = -1+i

Solve for all complex roots

then do the same for conjugate squared?

 

[Dick]

Given z = 1 + i,

Find all complex solutions to z^{2} + Conjugate:z^{2} = 0

I have come up with a way to solving this but it doesn't make any sense.

would it be:
z^{2} + 1-i = 0

z^{2} = -1+i

Solve for all complex roots

then do the same for conjugate squared?

Finding all complex solutions to z^2+conjugate(z^2)=0 makes a bit of sense. Adding "when z=1+i" makes it make no sense unless you just want to show (1+i)^2+(1-i)^2=0. Or do you just want to solve (1+i)^2+conjugate(z^2)=0??