What is the significance of [e^([pi]i)]+1=0 in mathematics?

[mathwonk]

im just saying there is essentially no other way to map the plane onto the punctured plane with derivative non zero, except to go around and around, so it has to hit the same point more than once, i.e. it hits 1 in finitely often, and also -1.

i see it like a spiral staircase.

 

[widewombat]

Beautiful and useful too, phasors for AC circuit analysis are based on Euler's identity.