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  2. Euler's identity - Wikipedia

    en.wikipedia.org/wiki/Euler's_identity

    The number e (e = 2.71828...), also known as Euler's number, which occurs widely in mathematical analysis The number i , the imaginary unit such that i 2 = − 1 {\displaystyle i^{2}=-1} The equation is often given in the form of an expression set equal to zero, which is common practice in several areas of mathematics.

  3. Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Euler's_formula

    The formula is still valid if x is a complex number, and is also called Euler's formula in this more general case. [1] Euler's formula is ubiquitous in mathematics, physics, chemistry, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics". [2] When x = π, Euler's formula ...

  4. Integration using Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Integration_using_Euler's...

    Using Euler's formula, any trigonometric function may be written in terms of complex exponential functions, namely and and then integrated. This technique is often simpler and faster than using trigonometric identities or integration by parts , and is sufficiently powerful to integrate any rational expression involving trigonometric functions.

  5. Complex logarithm - Wikipedia

    en.wikipedia.org/wiki/Complex_logarithm

    Such complex logarithm functions are analogous to the real logarithm function: >, which is the inverse of the real exponential function and hence satisfies e ln x = x for all positive real numbers x. Complex logarithm functions can be constructed by explicit formulas involving real-valued functions, by integration of 1 / z {\displaystyle 1/z ...

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  7. NYT ‘Connections’ Hints and Answers Today, Sunday, December 15

    www.aol.com/nyt-connections-hints-answers-today...

    Spoilers ahead! We've warned you. We mean it. Read no further until you really want some clues or you've completely given up and want the answers ASAP. Get ready for all of today's NYT ...

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