Calculator for the Absolute Values

Name: Calculator for the Absolute Values
Author: Jürgen Kummer

Find the absolute value of rational and complex numbers. The absolute value function measures the distance of a number from zero, the notation is |-1| = 1. Please enter complex numbers in the form a+bi, e.g. 2+2i or -2-2i. The absolute value of a complex number is calculated as |a+bi| = √ a² + b² . At input values, please enter one or more numbers separated by spaces, maximum 100 numbers. Decimal separator can be , or . be. In the case of complex numbers, the amount is rounded to the specified number of decimal places.

Example: the absolute values of the three numbers 2, -3, and 4-5i are 2, 3, and 6.403. The first number is a positive number and therefore equal to its absolute value; the second number is a negative number and therefore is its absolute value multiplied by minus one. The third, a complex number, is calculated using the formula above. This is also the formula for the famous Pythagorean theorem, because real and imaginary numbers are perpendicular to each other, like the sides in a right triangle, to which the Pythagorean theorem refers. Complex numbers consist of a real part and an imaginary part. If their two ends are connected, a hypotenuse with the length of the absolute value results in the complex number plane. The complex number, however, is obtained by rotating this hypotenuse 90 degrees on the number plane and placing its start at the origin.

The absolute is a mathematical quantity. Physically, it can be interpreted as something that has a direction, and for which this direction should be removed in order to determine only the dimension of this quantity. Examples of such quantities are force, motion, or speed. These work in a direction, this direction is irrelevant for some calculations, but not for others. Of course, it is impossible to say in general terms when an absolute value is the relevant quantity and when it is not.

Last updated on 09/07/2025. Author: Jürgen Kummer