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    Euler's identity

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    Recall the Taylor series Sum(x^n/n!). The same series can be used to define e^z for a complex number z=a+bi.
    Use the Taylor series to show that exp(iy) = cos(y) + i sin(y) for any real number y. To do this substitute iy into the series and compute several terms. Look for patterns.

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    https://brainmass.com/math/real-analysis/eulers-identity-27769

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    The solution demonstrates how to utilize Taylor series to obtain the famous Euler's identity.

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