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.