Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am trying to show that $e^{z+a}=e^ze^a$ where $a,z\in\mathbf{C}$ by using the fact that if $f,g$ are analytic on a region of $\mathbf{C}$ then $f=g$ if and only if the set $Z=\{z\in G: f(z)=g(z)\}$ has a limit point in $G$.

I know this result can be shown by other methods, but I want it done this way. It is frustrating me because I thought there would be a quick obvious answer. I tried using the fact that it holds for real numbers, but since $a\in\mathbf{C}$, I didn't get very far.

share|cite|improve this question
up vote 5 down vote accepted

First fix $a$ real and use that it holds for all real $z$ to conclude that it holds for all complex $z$. Then fix complex $z$ and use the fact that it holds for all real $a$ (which you just showed) to show that it holds for all complex $a$. I.e., just apply the argument twice.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.