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Complex Numbers Part Imaginary, but Really Simple

In this BLOSSOMS lesson, Professor Gilbert Strang introduces complex numbers in his inimitably crystal clear style. The class can go from no exposure to complex numbers all the way to Euler’s famous formula and even the Mandelbrot set, all in one lesson that is likely to require two 50-minute class sessions. Complex numbers have the form x + iy with a "real part" x and an "imaginary part" y and that famous imaginary number i, where i is the unreal square root of -1. Professor Strang shows that we should not worry about i, just work with the rule i^2 = -1. Professor Strang can hardly control his excitement as he presents these results to the class. That enthusiasm is bound to transfer over to the students. The breaks between video segments challenge the students to work through examples, assuring that they have captured the essence of the previous discussion of complex numbers. The lesson sets the foundation for the students to move further in their understanding and working with complex numbers.