Question

For $z$ being complex number prove that $\overline{e^z}=e^{\overline{z}}$.

Answer 1

For $z$ being complex number we have,

$e^z=e^x(\cos y+i\sin y)$.

Now,

$\overline{e^z}=e^x(\cos y-i\sin y)=e^x\left(\cos \right(-y)+i\sin (-y\left)\right)=e^{\overline{z}}$.