freeCodeCamp/guide/english/mathematics/eulers-formula/index.md

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title: Eulers Formula
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## Eulers 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.

 e^(ipi)+1=0, 

A famous joke for mathematicians is "How many mathematicians does it take to change a light bulb?" and answers "-e^(ipi)" 
Can you tell what the answer is?

This is often used when dealing with complex numbers in exponential form. 

![img](https://upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Euler%27s_formula.png/300px-Euler%27s_formula.png)

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#### More Information:
[Mathworld](http://mathworld.wolfram.com/EulerFormula.html)
[Wikipedia](https://en.wikipedia.org/wiki/Euler%27s_formula)