# direct computation

Show by direct computation that $\mid$ (2 $\overline{z}$+5)( $\sqrt{2}$ - i) $\mid$ = $\sqrt{3}$ $\mid$ 2z+5 $\mid$
Just note that $|zw|=|z||w|$ and $\overline{2\overline{z}+5}=2z+5$.