Modulus of Complex Number Calculator
Use this calculator to quickly find the modulus (or absolute value) of any complex number in the form a + bi. It helps students, engineers, and mathematicians determine the magnitude of complex numbers for analysis, graphing, and calculations involving polar form. Just enter the real and imaginary parts and get the result instantly.
Modulus of a Complex Number Calculator
Modulus of a Complex Number Formula
$$|z| = |a + bi| = \sqrt{a^2 + b^2}$$
To calculate the modulus of a complex number $$z = a + bi$$, square the real part $$a$$, square the imaginary part $$b$$, sum them, and take the square root of the result.
The modulus of a complex number represents its distance from the origin in the complex plane. It’s useful in converting a complex number into polar form, solving equations, and performing operations such as multiplication or division in trigonometric form. For example, the modulus of $$3 + 4i is \sqrt{3^2 + 4^2} = 5$$. This calculator is especially handy in electrical engineering, physics, and complex analysis.