# How do you find the absolute value of imaginary numbers?

## Question:

How do you find the absolute value of imaginary numbers?

## Imaginary Numbers:

In mathematics, an imaginary number is a number that contains the number i, where i is the imaginary number, such that i2 = -1. Imaginary numbers take on the form a + bi, where a and b are real numbers, and b≠ 0.

The absolute value of an imaginary number, a + bi, can be found using the following formula.

• {eq}|a+bi|=\sqrt{a^{2}+b^{2}} {/eq}

For example, suppose we wanted to find the absolute value of the imaginary number 3 + 4i. In this imaginary number, a = 3 and b = 4. Thus, we plug these into our formula and evaluate to find the absolute value of 3 + 4i.

• {eq}|3+4i|=\sqrt{3^{2}+4^{2}}=\sqrt{9+16}=\sqrt{25}=5 {/eq}

We get that the absolute value of 3 + 4i is 5, and this illustrates how to find the absolute value of an imaginary number.