01 What is a Complex Number?

The first of a series of videos introducing complex numbers. It would be ideal for anyone starting the study of complex analysis. Basic ideas are illustrated with examples and the viewer is asked to try examples as reinforcement.
Initial discussion of types of numbers (Natural N, Integers Z, Rational Q and Real R) leads on to the topic of the nature of the roots of a quadratic equation. This leads naturally to a specific example and then to a definition of a complex number. The set C of complex numbers is then introduced.
The Real Part (Re z) and Imaginary Part (Im z) of a complex number are illustrated with an exercise for the viewer followed by detailed solutions.
Complex solutions of more quadratic equations are derived and calculations are made by substitution to show that they do indeed satisfy the equations.