Just to know

what's Euler identity please ?, i'am 16 and trying to understand it but can't, and what's it used for ?

#Math

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Euler's identity is the following equation: $e^{i\pi} + 1 =0$ where $e$ is the exponential number and the base of the natural logarithm, $\pi$ is the ratio of the circumference and the diameter of any circle and $i$ is the imaginary unit that satisfies $i^2=-1$ . If you want to know where it comes from (its derivation), you need to learn about advanced trigonometry and complex numbers.But if you know about the Taylor Expansion of sine, cosine and e, you can take a look at this website. Even if you don't know about the Taylor expansions, check the site out!(simply because it's cool!).

Mursalin Habib - 8 years ago

A generalized form is http://www.proofwiki.org/wiki/Euler's_Formula. We need to put θ=π in the identity

Lab Bhattacharjee - 8 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$