Is there any intuitive explanation for: $$e^{i\pi} + 1 = 0$$
About whether this question is a duplicate, what is asked for is not a proof but an explanation that helps with the not-so-intuitive aspects of the identity.
Asked
Active
Viewed 323 times
0
-
1$-1$ is one unit to the left ($\pi$ radians from the right, i.e. postive direction) of $0$? – martini Jun 18 '15 at 12:35
-
2What do you mean by "intuitive"? – Jun 18 '15 at 12:36
-
I am open to any interpretation of the word. – user55570 Jun 18 '15 at 12:38
-
2If you think of $e^{i \theta}$ as a clockwise rotation of angle $\theta$ radians or remember $e^{i \theta} = \cos \theta + i \sin \theta$, then $e^{i \pi}$ is fairly obviously $-1$ – Henry Jun 18 '15 at 12:40
-
See also Has anyone talked themselves into understanding Euler's identity a bit? – Zev Chonoles Jun 18 '15 at 12:46
-
Would this answer your question ? – Lucian Jun 18 '15 at 20:50
-
That is an interesting explanation. Thanks Lucian – user55570 Jun 19 '15 at 00:07
1 Answers
3
Unit vectors in the opposite direction along the real line in the complex plane add to zero.
John Molokach
- 1,885
- 15
- 19