Complex Numbers
In this lesson on complex numbers, mathematician Adrienne Duadee explains the concept of adding and multiplying points and numbers in the plane, highlighting the connection between geometry and algebraic geometry. Duadee also discusses how the square root of negative one, which previously had been deemed impossible, was given new meaning and purpose in mathematics through the invention of imaginary numbers. She defines the modulus and argument of a complex number and discusses how they change when multiplying two complex numbers. Lastly, Duadee introduces the concept of stereographic projection and how it relates to complex numbers.
Complex numbers and square roots of negative numbers are explained. Also, transforming the plane to include complex numbers is discussed.
- Complex Number Definitions - Complex number definitions and functions.
- Short Course on Complex Numbers - A short course on complex numbers, the complex plane, and operations with complex numbers.
- Complex Number Applications - A bunch of complex number java applications.
- Who is Adrien Douady?
- What are complex numbers?
- What are imaginary numbers?
- What do complex numbers look like geometrically?
- What is the square root of -1?
- How do you add and multiply complex numbers?
- How are complex numbers like vectors?
- What does a complex stereographic projection look like?
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Staff Review
This video shows very clearly and concisely what complex numbers are and what they mean geometrically using a number line and protractor. Complex numbers, their addition and multiplication are shown on a blackboard in a way analogous to vectors in the plane. Finally, a stereographic projection of the complex plane is shown. A truly great place to begin understanding complex numbers.
