# Absolute Value of a Number

Definition of the absolute value of real and complex numbers

The absolute value of a real or complex number is its distance to zero. This absolute value or simply modulus is always a nonnegative real number.

## Absolute value of a real number

Simply put, you obtain the absolute value of a real number by omitting the sign. If real numbers are displayed on a number line, the negative numbers are to the left of the zero point and the positive numbers to the right of the zero point.

The absolute value of a real number is the distance from the zero point on the number line. The absolute value of a real number $$x$$ is written as $$|x|$$, or as a function $$abs(x)$$.

The absolute value of $$3$$ is equal to $$3$$    $$|3| = 3$$

The absolute value of $$-3$$ is equal to $$3$$     $$|-3| = 3$$

The absolute value of $$0$$ is equal to $$0$$     $$|0|=0$$

## Absolute value of a complex number

The representation of vectors of a complex number always results in a right-angled triangle consisting 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 value of a complex number $$z = a + bi$$ is $$|z|=\sqrt{a^2+b^2}$$

The figure below shows the graphical representation of the complex number $$3 + 4i$$ an the absolute value $$|z| = 5$$.

## Absolute value in RedCrab Calculator

In the RedCrab Calculator, the Abs function returns the absolute value of a real or complex number.

Abs(-3)=3

Abs(3+4i)=5