Math Help - algebra complex

1. algebra complex

Hey guys,

I need to find the complex solution to this: (and I apologise for not using the tools to display this stuff properly, but i havent learnt them yet and am in a hurry).

Find complex solutions of:
3|z|^2 + z[with a bar on it]^2 + 2z = 0
I have no idea how to go about doing this one Ive never even seen anything like that.

Also, {z [is a member of] C | z = z[with a bar on it]}
Does this just mean the real number line, ie y = 0, because the only time a complex number can equal its conjugate is when it =s 0?

Thanks a lot.

2. Originally Posted by Flay
Hey guys,

I need to find the complex solution to this: (and I apologise for not using the tools to display this stuff properly, but i havent learnt them yet and am in a hurry).

Find complex solutions of:
3|z|^2 + z[with a bar on it]^2 + 2z = 0
I have no idea how to go about doing this one Ive never even seen anything like that.

Also, {z [is a member of] C | z = z[with a bar on it]}
Does this just mean the real number line, ie y = 0, because the only time a complex number can equal its conjugate is when it =s 0?

Thanks a lot.
Let $z = x + iy \Rightarrow \overline{z} = x - iy$. Then your equation becomes:

$(4x^2 + 2y^2 + 2x) + i(2xy + 2y) = 0$.

Therefore:

Equate real parts: $2x^2 + y^2 + x = 0$ .... (1)

Equate imaginary parts: $xy + y = 0$ .... (2)

Solve equations (1) and (2) simultaneously.

3. thanks very much for that