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so everyone loves Euleramp;#39;s formula for the complex exponential that is e to the I Theta is cosine theta plus I sine Theta but most proofs involve Taylor series well hereamp;#39;s one that doesnamp;#39;t first of all we set F of theta equal to e to the minus I Theta times cosine theta plus I sine Theta notice that F evaluated at zero is one furthermore if you take the derivative of f you get 0 meaning that the function f is a constant which means itamp;#39;s equal to its value at zero which is one then multiplying both sides by e to the I Theta gives us our result so had you seen this before and donamp;#39;t forget to subscribe