Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 want know if I will be able to say that follow expression is periodic. i.e $$e^{i x}=e^{ix+2i\pi n}?$$

where $n$ is a real number

share|cite|improve this question

The answer is yes, so long as $n$ is an integer. By Euler's formula, $e^{i\theta}=\cos(\theta)+i\sin(\theta)$ when $\theta$ is a real number. In particular, $e^{2i\pi n}=\cos(2\pi n)+i\sin(2\pi n)=1$. From this it follows that $e^{ix}=e^{ix}e^{2i\pi n}=e^{i(x+2\pi n)}$. Note that it also follows that when $n$ is not an integer the equality will NOT hold.

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.