8. Euler's Formula. a. Using the MacLaurin series for f(x) = e^x we can show: EULER'S FORMULA: e^i? = cos ? + i sin ? Proof: e^x = e^i? = ?_{n=0}^{?} (i?)^n / n! = ?_{n=0}^{?} (i?)^{2n+1} / (2n + 1)! + (i?)^{2n} / (2n)! = odd terms even terms (Distribute the powers to complete the proof) b. Use EULER'S FORMULA to rewrite (simplify your answer) e^{i?} =
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