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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.

Absolute value of komplex number

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:

Formel zur Berechnung des Betrag einer komplexen Zahl

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

Betrag einer komplexen Zahl berechnen

Es gilt auch:

Absolutwert einer komplexen Zahl

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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Complex numbers

Basics of complex numbers
Computing with complex numbers
Addition and subtraction
Multiplication of complex numbers
Conjugate complex numbers
Division of complex numbers
Quadratic equations, complex numbers
Geometric representation
Geometric addition and subtraction
Absolute value of a complex number
The polar form of complex numbers
Calculate polar form
Convert polar form to normal
Multiplication in polar form
Division in polar form
   


           
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