# Thread: Complex number problem

1. ## Complex number problem

"Let z be a complex number and z (w/ a bar over it) be its conjugate. What are the four values of z for which zz(bar) and z^2 + z(bar)^2 = 6 ?"

I can't seem to a get an answer...I just did a lot of work and didn't get anything. I simplified it down to z^4 + 25 / z^2 = 6 and -z(bar) +6z(bar)^2 = 25, but that's all.

2. Originally Posted by ggeek101
"Let z be a complex number and z (w/ a bar over it) be its conjugate. What are the four values of z for which zz(bar) and z^2 + z(bar)^2 = 6 ?"

I can't seem to a get an answer...I just did a lot of work and didn't get anything. I simplified it down to z^4 + 25 / z^2 = 6 and -z(bar) +6z(bar)^2 = 25, but that's all.

$\displaystyle z=a+bi$
$\displaystyle \bar{z}=a-bi$

$\displaystyle z^2=a^2+2abi-b^2$
$\displaystyle \bar{z} ^2=a^2-2abi-b^2$

$\displaystyle z^2+\bar{z}^2=2a^2-2b^2=6$

$\displaystyle z\bar{z}=a^2+b^2=6$

So solve $\displaystyle a^2-b^2=3$ and $\displaystyle a^2+b^2=6$

3. Wow, I over thought this problem. I like your approach. Thanks!

4. no problemo.... i took it further and i believe the answers are not pretty, just so you're aware