Скачать или смотреть What is a Complex Number?

What is a complex number—and why is it more than just math trivia? In this video, we explore the symbolic, geometric, and vector interpretations of complex numbers, like z=4+3i, where i^2=-1 You'll learn: 1) How to break a complex number into its real and imaginary parts. 2) How to graph complex numbers in the complex plane (ℝ²). 3) How complex numbers naturally relate to vectors. 4)How this visual approach helps with arithmetic and complex functions. Along the way, we connect these ideas to tools like Mathematica and build intuition that sets the stage for complex analysis and multivariable calculus.

📌 Concepts Covered: 1) Re(z) and Im(z) notation. 2) Complex numbers as points and vectors. 3) The complex plane and ℂ vs. ℝ². 4) Using Mathematica to plot and analyze complex numbers

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🎓 Start with video 1:    • The MOST INTERESTING Basic Fact About the ...   (The MOST INTERESTING Basic Fact About the IMAGINARY UNIT i (Integer Powers of i Cycle))

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Visual Complex Analysis, by Tristan Needham: https://amzn.to/4d18FMP.

#complexnumbers #complexanalysis #vector

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(0:00) Complex Analysis video series
(0:41) Example complex number z=4+3i, where i^2=-1
(1:13) Real Part Re(z) and Imaginary Part Im(z) are both real numbers
(2:37) Plot in Complex Plane (plot 4+3i as the point with rectangular coordinates are (4,3))
(3:56) Plot -2+i in the Complex Plane (coordinates are (-2,1))
(5:06) Complex numbers as Vectors in the plane (position vectors for the given points)
(7:15) Set of complex numbers ℂ, described with set-builder notation
(8:03) Correspondence with real plane ℝ²
(9:01) Mathematica functions: Re, Im, ComplexListPlot, ReIm, ListPlot


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