Friday, 3 January 2014

calculus - Why Euler's formula is true?











I need to know why Euler's formula is true? I mean why is the following true:
eix=cos(x)+isin(x)


Answer



Hint: Notice sin(x)=xx33!+x55!x77!+..... and icos(x)=iix22!+ix44!ix66!+.... Now add them and use the fact that i2=1, i3=i, i4=1. You should obtain eix. Also notice: ex=1+x+x22!+x33!+.......


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