Improvements in wording and notation. (#27370)

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Andrew Mackie
2019-05-16 22:54:15 -07:00
committed by Parth Parth
parent c50fa87df3
commit f7cbf7494b

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---
title: Eulers Formula
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## Eulers Formula
## Euler's Formula
Eulers Formula is a mathematical identity which states that (for any value of x):
e^(ix)=cosx+isinx
This is of interest because of the following case:
When x=pi, Euler's Formula gives the beautiful identity invovling pi, e, and i.
Euler's Formula is a mathematical identity which states that, for any value of <em>x</em> (and where <em>e</em> is the base of the natural logarithm and <em>i</em> is the square root of -1):
e^(ipi)+1=0,
<em>e</em><sup><em>ix</em></sup> = cos <em>x</em> + <em>i</em> sin <em>x</em>
A famous joke for mathematicians is "How many mathematicians does it take to change a light bulb?" and answers "-e^(ipi)"
Furthermore, when <em>x</em> = <em>&pi;</em>, Euler's Formula results in the following beautiful identity relating <em>&pi;</em>, <em>e</em>, and <em>i:</em>
<em>e</em><sup><em>i&pi;</em></sup> + 1 = 0
A famous joke for mathematicians answers the question "How many mathematicians does it take to change a light bulb?" with "<em>-e</em><sup><em>i&pi;</em></sup>".
Can you tell what the answer is?
This is often used when dealing with complex numbers in exponential form.