Euler's identity - properHoc

Using Euler’s formula we get that

${e^{i\pi }} = \cos (\pi ) + i\sin (\pi ) = - 1$

Which immediately leads to arguably the most beautiful identities in mathematics:

${e^{i\pi }} + 1 = 0$

A formula connecting five fundamental numbers in mathematics.

We also have that

${e^{i\pi /2}} = \cos (\pi /2) + i\sin (\pi /2) = i$

And

${e^{ - i\pi /2}} = \cos ( - \pi /2) + i\sin ( - \pi /2) = - i$

Last modified: Mar 16, 2019 @ 15:29