Find the image of the finite vertical strip $R: x=5 \to x=9, -\pi \leq y\leq \pi$ of z-plane under exponential function.
The things I tried:
$w = e^z = e^{(x+iy)} = e^x(cos y) + i e^x(sin y)$
$\implies w = u + iv$
$\implies u = e^x(cos y ), v = e^x(sin y)$
$(5,\pi) \implies (-e^5, 0)$
$(9,\pi) \implies (-e^9,0)$
How to proceed from here and find image?