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)=x−x33!+x55!−x77!+..... and icos(x)=i−ix22!+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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