Question

For $z=x+iy$ find the real and imaginary part of $e^z$.

Answer 1

For $z=x+iy$ we have,

$e^z$

$=e^{x+iy}$

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

So the real part and the imaginary parts are $e^x\cos y$ and $e^x\sin y$.