Módulo |z|

√(a²+b²).
Created by
Renato Passos, Eng. de Software
Reviewed by
Renato Passos, Eng. de Software

Last updated: Apr 18, 2026

|z|
5,0000

About this calculator

The complex number modulus calculator computes the absolute value or magnitude of a complex number z = a + bi. The modulus is given by the formula √(a² + b²), where a is the real part and b is the imaginary part of the complex number. This calculation is fundamental in various areas of mathematics and physics, especially in complex analysis and signal theory.

The calculator works simply: just enter the values of the real part (a) and the imaginary part (b) of the complex number. The calculator then applies the formula to calculate the modulus. For example, for the complex number z = 3 + 4i, the modulus is calculated as √(3² + 4²) = √(9 + 16) = √25 = 5.

It's essential to use this calculator in cases where precision is crucial, such as in engineering, physics, and other exact sciences calculations. Additionally, it's useful for students and professionals who need to quickly determine the modulus of complex numbers without having to perform manual calculations.

A common care when using this calculator is to ensure that the entered values are correct and are real numbers. Typing errors or use of non-numeric values can lead to incorrect results.

Frequently asked questions

What is the modulus of a complex number?

The modulus of a complex number z = a + bi is given by the formula √(a² + b²), representing the distance of the complex number from the origin in the complex plane.

How does the modulus calculator work?

Just enter the real and imaginary part values of the complex number, and the calculator will apply the formula to calculate the modulus.

In what situations is it important to calculate the modulus of a complex number?

In engineering, physics, and other exact sciences calculations, where precision is crucial, and in complex analysis and signal theory.

What precautions should I take when using the calculator?

Ensure that the entered values are correct and are real numbers.

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