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Concept

Absolute Value of a Complex Number

The absolute value of a complex number

z = a + b i

, also called the modulus, is the distance from the origin to the point

(a, b)

in the complex plane.

The number $z$ can be interpreted as a vector and therefore, its length can be calculated using the Distance Formula.

$∣ z ∣ = a^{2} + b^{2}$

For example, the absolute value of $3 - 4 i$ is $∣ 3 - 4 i ∣ = 3^{2} + (- 4)^{2} = 5 .$

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