Concept

Absolute Value of a Complex Number

The absolute value of a complex number z=a+bi, also called the modulus, is the distance from the origin to the point (a,b) in the complex plane.
Point (a,b) that represents a complex number z = a + bi is plotted in the complex plane. A vector is drawn from the origin to point (a,b) such that its magnitude is the modulus of z.

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


|z| = sqrt(a^2+b^2)

For example, the absolute value of 3-4i is |3-4i| = sqrt(3^2 + (-4)^2) = 5.

Exercises