# Euler's identity

Not what you're looking for? Search our solutions OR ask your own Custom question.

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.

See the attached file.

Â© BrainMass Inc. brainmass.com November 24, 2022, 11:53 am ad1c9bdddfhttps://brainmass.com/math/real-analysis/eulers-identity-27769

#### Solution Summary

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

$2.49