# Simple complex conjugate question

I am trying to find:

$$\overline{\frac{-i \Gamma}{2\pi}\log\left(\frac{a^2}{\overline z}-b\right)}$$

Notice the conjugate sign above the $z$ and that $z$ is complex.

$\Gamma , a,b$ are real constants

I am aware of that $\overline{\log(\overline {Z})}=\log(Z)$

I am just confused on how to write this conjugate. Can I just change the minus sign to a plus and remove the conjugate sign above the $z$?

Thanks

• yes sorry, I didn't know how to write pi in the format. – juper Apr 25 '17 at 21:53
• What is $\Gamma$? – Joe Apr 25 '17 at 21:56
• it is the strength of a vortex - so just a constant. Sorry, I should have explained this. – juper Apr 25 '17 at 21:56
• Are $a,b$ reals? – dxiv Apr 25 '17 at 21:56
• yes sorry, I shall clarify this all in the question. apologies all, – juper Apr 25 '17 at 22:00

$$\overline{\frac{-i \Gamma}{2\pi}\log\left(\frac{a^2}{\overline z}-b\right)}=\frac{i \Gamma}{2\pi}\log\left(\frac{a^2}{ z}-b\right)$$
• Yeah, it's not an obvious thing and I think people over-think it. Just replace all $i$'s by $-i$. – Cye Waldman Apr 26 '17 at 13:58