# Absolute value of a complex number

The absolute value of a complex number a + bi, also called the modulus of a complex number a + bi, is its distance from the origin on the complex number plane.

On the complex plane, the complex number a + bi is represented as a point (a, b) and the coordinate of the origin is (0, 0).

Just find the distance between (0,0) and (a,b)

We can use the distance formula to find the absolute value of a complex number.

$$Distance = \sqrt{(a-0)^{2}+(b-0)^{2}}$$
$$Distance = \sqrt{(a)^{2}+(b)^{2}}$$
$$|a + bi| = \sqrt{(a)^{2}+(b)^{2}}$$

## Two examples showing how to find the absolute value of a complex number.

Find the absolute value of the complex numbers 4 - 3i and 6i.

Notice that 6i = 0 + 6i.

$$|4 - 3i| = \sqrt{(4)^{2}+(-3)^{2}}$$
$$|4 - 3i| = \sqrt{16 + 9} = 5$$
$$|6i| = \sqrt{(0)^{2}+(6)^{2}}$$
$$|6i| = \sqrt{0 + 36} = 6$$

The figure below shows the distance for the complex number 4 - 3i in red and the distance for the complex number 6i in blue.

## Recent Articles

1. ### Calculate the Conditional Probability using a Contingency Table

Mar 29, 23 10:19 AM

Learn to calculate the conditional probability using a contingency table. This contingency table can help you understand quickly and painlessly.

2. ### Rational Numbers - Definition and Examples

Mar 15, 23 07:45 AM

To learn about rational numbers, write their decimal expansion, and recognize rational numbers that are repeating decimals and terminating decimals.