The famous formula ea+bi = ea(cos b + i sin b) is called Eulers Formula, after the Swiss

Chapter 7, Problem 175

(choose chapter or problem)

The famous formula

\(e^{a+bi}=e^{a}(\cos b+i\ \sin b)\)

is called Euler’s Formula, after the Swiss mathematician Leonhard Euler (1707–1783). This formula gives rise to the equation

\(e^{\pi i}+1=0\).

This equation relates the five most famous numbers in mathematics—\(0,\ 1,\ \pi,\ e,\) and \(i\)—in a single equation. Show how Euler’s Formula can be used to derive this equation. Write a short paragraph summarizing your work.

Text Transcription:

e^a+bi =e^a (cos b + i sin b)

e^pii +1=0

0, 1, pi, e

i

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