MIT Massachusetts Institute of Technology

Complex Numbers: Part Imaginary, but Really Simple

Gilbert Strang 
Professor of Mathematics
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139 USA

 
Lesson vetted and approved by CPALMS

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.

Professor Strang teaches Linear Algebra and Computational Science at MIT, and both of these classes are videotaped and available on MIT's OpenCourseWare ocw.mit.edu. He also writes research papers and textbooks on these subjects. Click here to read more about Professor Strang.

This site introduces you to all the Khan Academy resources available on Imaginary and Complex Numbers.
https://www.khanacademy.org/math/algebra2/complex-numbers-a2

This site, sponsored by the School of Wisdom, is entitled “The Mathematics of Chaos” and presents the basic math behind Chaos and the Mandelbrot set. 
http://www.fractalwisdom.com/science-of-chaos/the-mathematics-of-chaos/

This resource, presented by the Mathematics Network at the University of Toronto, provides an interesting discussion of Complex Numbers in real life.
https://www.math.toronto.edu/mathnet/questionCorner/complexinlife.html

This site, developed by the Oswego City School District Regents Exam Prep Center, presents an introductory glimpse of the application of complex numbers to electrical circuits that can be easily understood and manipulated by students. 
http://www.regentsprep.org/regents/math/algtrig/ato6/electricalresouce.htm

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