Find z given z̄² + zi = -i + 1

[blckndglxy]

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.

Homework Equations

The Attempt at a Solution

 

[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.

 

[ehild]

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.

Homework Equations

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.

 

[ehild]

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.

 

[blckndglxy]

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]

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]

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]

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,

 

[Bibatshu Thapa]

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!