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Consider the Maclaurin series for the real exponential function:$$ e^u = 1 + u + \frac{u^2}{2!} + \frac{u^3}{3!} + \frac{u^4}{4!} + \frac{u^5}{5!} + \dots $$By formally substituting \(u=ix\) and rearranging the terms, show how this series relates to the series for \(\cos(x)\) and \(\sin(x)\).
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