2
$\begingroup$

I am required to prove the following:

For any real number $k$, prove that the exponential function $e^z$ is a bijection ($z$ is a complex number) from the strip $a < im z \leq k+2pi$ to the complex plane minus the point $0$, $\Bbb C - \{0\}$.

Any hints please? Thanks!

  • 0
    Michael, yup, aa was intended to be k, fell asleep on the keyboard:p2012-08-26
  • 0
    It can't be *any* $k\in \mathbb{R}$, because what if $k=3$ and $im(z)=2$?2012-08-26

2 Answers 2