Complex Number Magnitude Calculator

Unravel the magnitude of complex numbers with ease. Enter the real and imaginary parts to instantly calculate the modulus and visualize it on the complex plane.

Enter Complex Number

A complex number is of the form a + bi, where a is the real part and b is the imaginary part.

Real Part (a):

Imaginary Part (b):

Result

Magnitude (Modulus):

The magnitude of a complex number z = a + bi is calculated using the formula:

$$|z| = \sqrt{a^2 + b^2}$$

Visual Representation on Complex Plane

Understanding Complex Number Magnitude

In mathematics, a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1. The real part is a, and the imaginary part is b.

The magnitude (or modulus) of a complex number represents its distance from the origin (0, 0) in the complex plane. It's a real number that gives the "size" or "absolute value" of the complex number.

Formula: For a complex number z = a + bi, the magnitude |z| is calculated as:

$$|z| = \sqrt{a^2 + b^2}$$

Use Cases: Complex number magnitudes are crucial in various fields such as electrical engineering (AC circuit analysis), quantum mechanics, signal processing, and more. They help in understanding the strength or intensity of complex quantities.