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32.1: Комплексні числа
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\[ \begin{align} e^{i \theta} &= 1 + i\theta + \dfrac{(i\theta)^2}{2!} + \dfrac{(i\theta)^3}{3!} + \dfrac{(i\theta)^4}{4!} + \dfrac{(i\theta)^5}{5!} ... \label{A.19a} \\[4pt] &= 1 + i\theta - \dfrac{\...\[ \begin{align} e^{i \theta} &= 1 + i\theta + \dfrac{(i\theta)^2}{2!} + \dfrac{(i\theta)^3}{3!} + \dfrac{(i\theta)^4}{4!} + \dfrac{(i\theta)^5}{5!} ... \label{A.19a} \\[4pt] &= 1 + i\theta - \dfrac{\theta^2}{2!} - \dfrac{i\theta^3}{3!} +\dfrac{\theta^4}{4!} +\dfrac{i\theta^5}{5!} ... \label{A.19b} \\[4pt] &= \left( 1 - \dfrac{\theta^2}{2!} + \dfrac{\theta^4}{4!} \right) + i \left(\theta - \dfrac{i\theta^3}{3!}+\dfrac{i\theta^5}{5!} \right) \label{A.19c} \\[4pt] &= \cos \theta + i\sin \theta \l…