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A complete guide to the basics of complex numbers. Feel free to pause and catch a breath if you feel like it - it's meant to be a crash course! Complex numbers are useful in basically all sorts of applications, because even in the real world, making things complex sometimes, oxymoronically, makes things simpler. This is the basis for a lot of physical applications, like circuit analysis, as well as slightly more far-fetched like Fourier analysis or Laplace transforms. Even for pure mathematicians, this is very useful due to its algebraic closure, and the beautiful world of complex analysis. As said before in the previous video, complex analysis is an extremely powerful tool that everyone should be excited about! This video will cover basically all of the topics you will ever learn in a normal course in complex numbers, or things considered basics in complex analysis, namely, Cartesian and polar ways of representation, Euler's formula and identity, the different operations of complex numbers, including compl
