It started out with me trying to find all the values to equations like, $x^\pi=1$ but then i thought, is there a formula that will apply to any power of $x$. So, i came up with a formula for one. Here it is, $$x^n = 1$$ $$x= e^{\frac{2i\pi k}{n}},k\in \mathbb{Z}$$

Iam unsure if it is completely correct but it seems to be.

  • $\begingroup$ Indeed it is true that, for all $n\in\Bbb Z\setminus \{0\}$ and $x\in \Bbb C$, $$x^n=1\Leftrightarrow \exists k\in\Bbb Z, x=e^{2ik\pi /n}.$$ $\endgroup$ Commented Oct 17, 2023 at 7:35
  • $\begingroup$ How do I publish the proof? $\endgroup$ Commented Oct 17, 2023 at 10:17
  • $\begingroup$ The fact has been known for centuries and it's taught in the first courses of university curricula. There is no research interest in other proofs (true or purported). $\endgroup$ Commented Oct 17, 2023 at 10:33


You must log in to answer this question.

Browse other questions tagged .