Question

Find the modulus of the complex number $e^z$ for $z=x+iy$.

Answer 1

For $z=x+iy$ we have, $e^z=e^x(\cos y+i\sin y)$.

Now, $|e^z|=\sqrt{e^{2x}({\cos }^{2}y+{\sin }^{2}y)}=e^x.$