Thread: Understanding a formula

i^-i=

I read here, The number e, that this formula is not understood.

"In 1864 Benjamin Peirce had his picture taken standing in front of a blackboard on which he had written the formula above. In his lectures he would say to his students:-

Gentlemen, we have not the slightest idea what this equation means, but we may be sure that it means something very important.:

Is there a meaning to this equation?

I tried to understand it with my calculator, but failed horribly.
i^-i=
With my limited understanding of i, that makes absolutely sense to me whatsoever.

I'm doing a research paper for undergraduate admissions into Cal Tech about 'e'.


Thanks!

Originally Posted by Truthbetold

i^-i=

I read here, The number e, that this formula is not understood.

"In 1864 Benjamin Peirce had his picture taken standing in front of a blackboard on which he had written the formula above. In his lectures he would say to his students:-

Gentlemen, we have not the slightest idea what this equation means, but we may be sure that it means something very important.:

Is there a meaning to this equation?

I tried to understand it with my calculator, but failed horribly.
i^-i=
With my limited understanding of i, that makes absolutely sense to me whatsoever.

I'm doing a research paper for undergraduate admissions into Cal Tech about 'e'.


Thanks!

are you familiar with Euler's formula? .

with that we can see that for any integer . since all will give the same value, we can take one, is the nicest.

thus we have,