Khan Academy
11:27
Khan Academy
Aug 14, 2016
Khan AcademySal Khan
The Euler's formula for any real number x is e^(ix) = cos(x) i sin(x), where e is the base of the natural logarithm (approximately 2.718), i is the imaginary unit (i = √(-1)), and cos and sin are the trigonometric functions. To visualize Euler's formula in the complex plane, consider the following: - The complex plane is a 2D plane where the x-axis represents the real part of a complex number, and the y-axis represents the imaginary part. - The expression e^(ix) represents a point on the unit ci
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The Euler's formula for any real number x is e^(ix) = cos(x) i sin(x)…
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Euler’s magic in one simple formula: V - E F = 2. (Vertices - Edges Faces = 2) Euler’s Polyhedron Formula: V - E F = 2, a fundamental equation in geometry that applies to all convex polyhedra. It breaks down how the number of Vertices (V), Edges (E), and Faces (F) are always connected through this elegant relationship. The goal is to spark curiosity and show the beauty of mathematics through a simple yet powerful concept. #trending #trendingnow #trendingreels #trendingaudio #explorepage #explore
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Euler’s magic in one simple formula: V - E F = 2. (Vertices - Edges Face…
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📌Euler's formula is a fundamental equation in complex analysis that shows a deep connection between exponential functions and trigonometric functions. It states that *e* raised to the power of *i* times *x* equals the cosine of *x* plus *i* times the sine of *x*. In simple terms, it expresses how complex exponentials can represent circular motion. This formula is widely used in engineering, physics, and mathematics because it elegantly links exponential growth, rotation, and wave behavior in a
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