RedCrab Math Tutorial

# The absolute value of a complex number

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:

Calculation of the absolute value of the complex number z = 3 - 4i:

Es gilt auch:

Note that the absolute value at 3 + 4i and 3 - 4i is positive. The absolute value of complex and real numbers is always a positive value.

In most programming languages or math software, the name Abs is used for the function for determining the absolute value.

## Complex numbers

Basics of complex numbers
Computing with complex numbers
Multiplication of complex numbers
Conjugate complex numbers
Division of complex numbers