proof of addition formula of exp
The addition formula
of the complex exponential function may be proven by applying Cauchy multiplication rule to the Taylor series expansions (http://planetmath.org/TaylorSeries) of the right side factors (http://planetmath.org/Product). We present a proof which is based on the derivative of the exponential function.
Thus we see that the product must be a constant . If we choose specially , we obtain:
If we denote , the preceding equation reads . Q.E.D.
|Title||proof of addition formula of exp|
|Date of creation||2013-03-22 16:32:03|
|Last modified on||2013-03-22 16:32:03|
|Last modified by||pahio (2872)|
|Defines||addition formula of exponential function|