I have to show that

$\displaystyle |(2\overline{z}+5)(\sqrt{2}-i)|=\sqrt{3}|2z+5|$

So far, I have

$\displaystyle |(2\overline{z}+5)(\sqrt{2}-i)|=|2\overline{z}+5||\sqrt{2}-i)|$

My sol'n book then says this is equal to

$\displaystyle |\overline{2z+5}|\sqrt{2+1}$

I understand that for the second term they are just finding the length, but I don't understand how

$\displaystyle |2\overline{z}+5|=|\overline{2z+5}|$.

Can anyone explain the math behind that?