Difference between revisions of "Euler's Formula"
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| − | [[Euler]]'s formula is the following identity in complex analysis making use of the [[imaginary number]] <math>i</math>: | + | '''[[Euler]]'s formula''' is the following identity in complex analysis making use of the [[imaginary number]] <math>i</math>: |
:<math>e^{i\phi} = \cos \phi + i\sin \phi \!</math> | :<math>e^{i\phi} = \cos \phi + i\sin \phi \!</math> | ||
| − | < | + | |
| − | [[ | + | ==Euler's Identity== |
| + | The formula can be used to derive an equation known as Euler's identity: | ||
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| + | :<math>e^{i\pi} + 1 = 0 \!</math> | ||
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| + | '''''This is called the most beautiful equation in all of mathematics''''', because it equates the five most common mathematical constants in a perfectly elegant manner. | ||
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| + | ==See also== | ||
| + | *[[De Moivre's Theorem]] | ||
| + | *[[Leonard Euler]] | ||
| + | *[[Arbitrariness or Ambiguity in the Definition of the Imaginary Unit in Mathematics]] | ||
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| + | [[Category:Mathematics]] | ||
Latest revision as of 02:54, May 5, 2021
Euler's formula is the following identity in complex analysis making use of the imaginary number :
Euler's Identity
The formula can be used to derive an equation known as Euler's identity:
This is called the most beautiful equation in all of mathematics, because it equates the five most common mathematical constants in a perfectly elegant manner.