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Nea
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Analyze by Maclaurin formula:
$e^{ix}$
$e^{ix}$
The Maclaurin Formula for $e^{ix}$ is given by $e^{ix} = \sum_{n=0}^\infty \frac{(ix)^n}{n!} = 1 + ix + \frac{(ix)^2}{2!} + \frac{(ix)^3}{3!} + \cdots$
The Maclaurin Formula for $e^{ix}$ can be derived using the Taylor Series Expansion of $e^x$ at $x=0$, and then replacing $x$ with $ix$ to obtain the complex form.
The Maclaurin Formula for $e^{ix}$ is significant because it allows us to express complex exponential functions in a simplified form, making it easier to perform calculations and solve problems.
The Maclaurin Formula for $e^{ix}$ is an infinite series, so the accuracy depends on the number of terms used in the calculation. The more terms used, the more accurate the result will be.
The Maclaurin Formula for $e^{ix}$ is used in various fields of science and engineering, such as signal processing, quantum mechanics, and electrical engineering. It is also used in solving differential equations and in the study of complex analysis.