# Complex number and its conjugate problem help

1. Jun 29, 2017

### blckndglxy

1. The problem statement, all variables and given/known data
Given that a complex number z and its conjugate z¯ satisfy the equation z¯z¯ + zi = -i +1. Find the values of z.

2. Relevant equations

3. The attempt at a solution

2. Jun 29, 2017

### Bibatshu Thapa

Hey, I think z.z-=1 but what's with the zi thing. Can you upload the picture of your question? Its not clear enough.

3. Jun 29, 2017

### ehild

Hi blckndglxy, welcome to PF.

You have to show some attempt at solving the problem. Write z as z=x+iy, substitute into the equation z¯z¯ + zi = -i +1 and solve.

4. Jun 29, 2017

### ehild

You are not right, z.z- = |z|2, square of the magnitude of z. zi is z multiplied by i.

5. Jun 29, 2017

### blckndglxy

hello there.. so z¯ = x-iy right? so i have to replace the z¯ too right? sorry i'm still new and i'm clueless with this question..

6. Jun 29, 2017

### ehild

Yes. Replace z with x+iy and z- with x-iy.

7. Jun 29, 2017

### Ray Vickson

Writing $z = x+iy$ and $bar{z} = x - iy$, your equation becomes
$$|z|^2 = 1 - i - zi$$.
Can you see how the value of $x$ can be determined right away from this equation? That leaves you with the simpler problem of finding $y$.

8. Jun 29, 2017

### ehild

The original equation is z¯z¯ + zi = -i +1. z¯z¯ is not |z|2,

9. Jul 1, 2017

### Bibatshu Thapa

Thanks a lot. Well I had forgotten the fact you mentioned. Really HELPFUL!