0
$\begingroup$

Are there any non trivial properties unique of the imaginary numbers?

By trivial I mean stuff like $\bar a=-a$.

$\endgroup$
  • 6
    $\begingroup$ It's still not clear to me what would qualify as non-trivial. $\endgroup$ – Michael Albanese Apr 19 '15 at 22:07
  • $\begingroup$ For example $z^2 \in (-\infty, 0)$? $\endgroup$ – Robert Israel Apr 19 '15 at 22:10
  • $\begingroup$ Like $\lvert e^a \rvert = 1$ precisely when the real part of $a$ is $0$? $\endgroup$ – pjs36 Apr 19 '15 at 22:11
  • $\begingroup$ The title says "pure imaginary numbers" but the body of the question says "imaginary numbers". Which is it? $\endgroup$ – bof Apr 19 '15 at 22:53
  • $\begingroup$ @bof Pure I meant a complex number that has real part = 0. $\endgroup$ – YoTengoUnLCD Apr 19 '15 at 22:54
1
$\begingroup$

$|e^z| = 1$ for $z$ purely imaginary.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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