# Complex number and its conjugate problem help

## Homework Statement

Given that a complex number z and its conjugate z¯ satisfy the equation z¯z¯ + zi = -i +1. Find the values of z.

## The Attempt at a Solution

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.

ehild
Homework Helper

## Homework Statement

Given that a complex number z and its conjugate z¯ satisfy the equation z¯z¯ + zi = -i +1. Find the values of z.

## The Attempt at a Solution

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.

• Bibatshu Thapa
ehild
Homework Helper
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.
You are not right, z.z- = |z|2, square of the magnitude of z. zi is z multiplied by i.

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.

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..

ehild
Homework Helper
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..
Yes. Replace z with x+iy and z- with x-iy.

Ray Vickson
Homework Helper
Dearly Missed
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..
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##.

ehild
Homework Helper
Writing ##z = x+iy## and ##bar{z} = x - iy##, your equation becomes
$$|z|^2 = 1 - i - zi$$.
The original equation is z¯z¯ + zi = -i +1. z¯z¯ is not |z|2,

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