Theory

Theory 1

A complex number can be represented in the plane as the point with Cartesian coordinates . The coefficient of “” determines the vertical coordinate, and the coefficient of “” determines the horizontal coordinate.

Let us be given a complex number .

The “real part” and “imaginary part” of can be extracted with designated functions:

The polar data (radius and angle) have special names and notations for complex numbers:

Using this notation, we see that product with the conjugate gives square of modulus: