Complex Numbers as Matrices

In this video, we'll learn how to view a complex number as a 2x2 matrix with a special form. We'll also see that there is a matrix version for the number 1 and a matrix representation for the imaginary unit, i. Furthermore, the matrix representation for i has the defining feature of the imaginary unit in that it squares to -1. We'll also explore other features of complex numbers that tie into matrix operations, such as the determinant and transpose. Euler's formula even has a sensible interpretation in matrix algebra and we'll see an example of a matrix exponential.