
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. 
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