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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Euler’s formula beautifully connects exponential functions with trigonometry. In this visualization, you can see how the real and imaginary parts dance together on the unit circle. What does this formula mean to you? Can you think of a real-world application or a question it raises? Share your thoughts in the comments, like the reel if it sparked your curiosity, and tag someone who loves math! صيغة أويلر تربط بشكل رائع بين الدوال الأسية وعلم المثلثات. في هذا التصور، يمكنك أن ترى كيف تتفاعل الأجز
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