28 Apr
2006
28 Apr
'06
6:11 p.m.
Emeric wrote: << On Fri, 28 Apr 2006, Steve Gray wrote:
... On these scores, e^(i pi)+1=0 is unbeatable.
I am sure that I am missing here something. What is the definition of e^(x+iy) ? Isn't it e^(x+iy)=e^x (cos y + i sin y) ?
Of course not: e^x began life as the inverse of tne integral from 1 to x > 0 of 1/x; sine and cosine began their lives as projections of a point moving around the circle at constant speed. Then these were extended in the unique natural way to the complex numbers. Then voila! -- an unexpected connection is made. --Dan