Hence why it is the square modulus...

A more formal way of describing |z| is as trivial in trigonometry: using the Pythagorean theorem, sqrt(x^2 + y^2), we get the distance, modulus or magnitude of a complex number. The argument, or phase, theta, of a complex number, is given by atan2(z), or atan(y/x). And the magnitude is given as sqrt(cos(theta)^2 + sin(theta)^2), and z = r*exp(i*theta), where r is the magnitude of z, and i = sqrt(-1). It also equals to r*(cos(theta) + i*sin(theta)), with Euler's identities, yielding the polar coordinates.

Hence why it is the square modulus...
A more formal way of describing |z| is as trivial in trigonometry: using the Pythagorean theorem, sqrt(x^2 + y^2), we get the distance, modulus or magnitude of a complex number. The argument, or phase, theta, of a complex number, is given by atan2(z), or atan(y/x). And the magnitude is given as sqrt(cos(theta)^2 + sin(theta)^2), and z = r*exp(i*theta), where r is the magnitude of z, and i = sqrt(-1). It also equals to r*(cos(theta) + i*sin(theta)), with Euler's identities, yielding the polar coordinates.