Improvements in wording and notation. (#27370)
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Parth Parth
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title: Eulers Formula
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---
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## Eulers Formula
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## Euler's Formula
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Eulers Formula is a mathematical identity which states that (for any value of x):
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e^(ix)=cosx+isinx
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This is of interest because of the following case:
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When x=pi, Euler's Formula gives the beautiful identity invovling pi, e, and i.
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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):
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e^(ipi)+1=0,
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<em>e</em><sup><em>ix</em></sup> = cos <em>x</em> + <em>i</em> sin <em>x</em>
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A famous joke for mathematicians is "How many mathematicians does it take to change a light bulb?" and answers "-e^(ipi)"
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Furthermore, when <em>x</em> = <em>π</em>, Euler's Formula results in the following beautiful identity relating <em>π</em>, <em>e</em>, and <em>i:</em>
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<em>e</em><sup><em>iπ</em></sup> + 1 = 0
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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>iπ</em></sup>".
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Can you tell what the answer is?
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This is often used when dealing with complex numbers in exponential form.
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