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seanieg89

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It is a pretty immediate fact from the way the the trig functions and the exponentials are defined in higher mathematics (read about power series if you are really interested).
 

hup

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there is the noob way of proving it

y = cisx
y' = icisx = iy

dy=iy (dx)
dy/(iy) = dx
integrate and find constant you get

e^ix = cosx + i sinx
 

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