i^-i= $\displaystyle \sqrt{e^\pi}$

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= $\displaystyle \sqrt{e^\pi} =about 4.787$

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!