In the article on the complex plane, it was described that every complex number z can be clearly assigned a vector.
The length of the vector has a special name in the complex numbers.
We call it the absolute value of the complex number.

The figure below shows the graphical representation of the complex number \(3 + 4i\).

The representation with vectors always results in a right triangle,
which consists of the two catheters \(a\) and \(b\) and the hypotenuse \(z\).
The absolute value of a complex number corresponds to the length of the vector.

The absolute value of the complex number \(z = a + bi\) is

\(|z|=\sqrt{a^2+b^2} = \sqrt{Re^2 + Im^2}\)

Calculation of the absolute value of the complex number \(z = 3 - 4i\)