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11:27
Khan Academy
Sal Khan
Euler's formula & Euler's identity
Euler's Formula, e^(ix) = cos(x) + i*sin(x), and Euler's Identity, e^(iπ) + 1 = 0, are incredible math discoveries. They connect e, i, and pi through Maclaurin series of cos(x), sin(x), and e^x. These formulas reveal a deep, mysterious connection between important numbers in math.
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Euler’s identity is often celebrated as one of the most beautiful equations in mathematics: e^(iπ) 1 = 0. It brings together five of the most important constants—e, i, π, 1, and 0—into a single elegant formula. What makes this identity so remarkable is how it links fundamental concepts from different branches of mathematics: e, the base of natural logarithms from calculus; π, the circle constant from geometry; and i, the imaginary unit from complex numbers. The equation essentially reveals a dee
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