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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