(adsbygoogle = window.adsbygoogle || []).push({}); Complex equation with "z"

1. The problem statement, all variables and given/known data

[tex]z^2-\bar z |z|= 1[/tex]

2. Relevant equations

Complex numbers

3. The attempt at a solution

[tex](a+ib)^2-(a-ib)\sqrt{a^2+b^2} = 1[/tex]

[tex]a^2-b^2+2iab-a\sqrt{a^2+b^2}+ib\sqrt{a^2+b^2} = 1[/tex]

I separate the real part from the imaginary part.

[tex]

\left\{\begin{matrix}

2iab+ib\sqrt{a^2+b^2}=0

\\

a^2-b^2-a\sqrt{a^2+b^2}=1

\end{matrix}\right.

[/tex]

One solution of the first is [itex]b=0[/itex]

[tex]

\left\{\begin{matrix}

2a+\sqrt{a^2+b^2}=0, \ 3a^2=b^2

\\

a^2-b^2-a\sqrt{a^2+b^2}=1

\end{matrix}\right.

[/tex]

So I basicalliy have two solution from the first eq.

1) [itex]b=0[/itex]

2)[itex] 3a^2=b^2[/itex]

If you plug these results in the seconds I don't get anything...

Either I get [itex]a^2-a^2=1[/itex] or [itex]-a^2=1[/itex] which has no solution since [itex]a \in \mathbb{R}[/itex]

Could anyone confirm this equation has no solution. It's supposed to have one since it was part o an exam.

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Complex equation with z

**Physics Forums | Science Articles, Homework Help, Discussion**