Theorems in complex analysis | Mathematical identities | E (mathematical constant) | Exponentials

Euler's identity

In mathematics, Euler's identity (also known as Euler's equation) is the equality where e is Euler's number, the base of natural logarithms,i is the imaginary unit, which by definition satisfies i2 = −1, andπ is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler's formula when evaluated for x = π. Euler's identity is considered to be an exemplar of mathematical beauty as it shows a profound connection between the most fundamental numbers in mathematics. In addition, it is directly used in a proof that π is transcendental, which implies the impossibility of squaring the circle. (Wikipedia).

Euler's identity
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Euler's Identity (Equation)

This video given Euler's identity, reviews how to derive Euler's formula using known power series, and then verifies Euler's identity with Euler's formula http://mathispower4u.com

From playlist Mathematics General Interest

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Euler Pronunciation: In Depth Analysis

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From playlist Fun and Amazing Math

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Euler's real identity NOT e to the i pi = -1

NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) I've got some good news and some bad news for you. The bad news is that Euler's identity e to the i pi =

From playlist Recent videos

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Euler's Identity Explanation

In this video, I am going to be showing you how to derive Euler's Formula and Identity. #breakthroughjuniorchallenge #breakthroughjuniorchallenge2020 EXTRA TIDBITS OF INFORMATION: - There are a few applications of Euler's Identity. One important use of it is when calculating AC current i

From playlist Summer of Math Exposition Youtube Videos

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Euler‘s identity e to the i pi = -1 and common sense

Euler's identity e to the i pi = -1 is a very general abstract algebraic identity. This video shows one concrete geometric realization of this famous equation starting from scratch. Can you find more? Using a line of thought expressed in Sir William Rowan Hamiltons "Elements of Quaternion

From playlist Summer of Math Exposition Youtube Videos

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Linear Algebra 21g: Euler Angles and a Short Tribute to Leonhard Euler

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From playlist Part 3 Linear Algebra: Linear Transformations

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Euler's formulas, Rodrigues' formula

In this video I proof various generalizations of Euler's formula, including Rodrigues' formula and explain their 3 dimensional readings. Here's the text used in this video: https://gist.github.com/Nikolaj-K/eaaa80861d902a0bbdd7827036c48af5

From playlist Algebra

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Someone asked me a question about Euler's Identity (e^iπ = --1)...

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From playlist Introduction to Complex Numbers

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A (very) Brief History of Leonhard Euler

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From playlist Mathematics named after Leonhard Euler

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YOU CAN'T USE EULER'S IDENTITY TO PROVE THE ANGLE SUM IDENTITIES! | Tricky Parts of Calculus, Ep. 4

I give multiple proofs of the angle sum identities sin(x+y) = sin(x)cos(y) + sin(y)cos(x) and cos(x+y) = cos(x)cos(y) - sin(x)sin(y) from different perspectives. I stress that a very common presentation of these formulas based on Euler's identity e^(ix) = cos(x) + i sin(x) is circular and

From playlist Math

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Are 3Blue1Brown and Khan Academy WRONG about Euler’s Formula? / [e to the i pi, e^(i*pi), beautiful]

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From playlist Misc.

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Marc Levine: Refined enumerative geometry (Lecture 2)

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Euler's Formula - Numberphile

Tom Crawford shows us some cool things about Euler's Formula... Check https://brilliant.org/numberphile for Brilliant and get 20% off their premium service (episode sponsor) More links & stuff in full description below ↓↓↓ Tom Crawford's website, with links to his work and other outreach:

From playlist Tom Crawford on Numberphile

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Numerical Integration of ODEs with Forward Euler and Backward Euler in Python and Matlab

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From playlist Engineering Math: Differential Equations and Dynamical Systems

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From playlist Recent videos

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Proof of Euler's Identity | Complex Numbers

Given any introduction to complex numbers, one sooner or later is exposed to Euler's formula (or Euler's identity), which expresses an exponential of an imaginary number in terms of the sum of two trigonometric functions. Many proofs are either technical or unenlightening and in most cases

From playlist Complex Analysis

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More resources available at www.misterwootube.com

From playlist Introduction to Complex Numbers

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From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory

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