The argument of a complex number complex(x,y) on the complex plane:
When a complex number is written in polar form
x + iy = r eiφ
then its argument is the real value φ in the exponent. It is calculated numerically using the atan2 function.
This example deliberately replicates some of the arithmetic of complex numbers of Math to avoid importing that entire library for a couple lines of code. It also encodes the tiny amount of mathematical notation in HTML to void importing all of MathJax.
Complete code for this example: