Complex Modulus Calculator
Find the modulus or absolute value of a complex number in rectangular or polar form. Shows exact radical output, squared modulus, real and imaginary parts, argument, and geometry.
What the complex modulus means
For English queries, complex modulus and absolute value of a complex number usually mean the same calculation: the distance from zero to the point a+bi on the Argand plane.
a is the real part and b is the imaginary part.
The squared modulus is useful for checking the result before taking the square root.
How the calculator handles input
- Enter a rectangular number such as 3+4i, 1-i, -2i, or sqrt(3)+i.
- Enter polar notation such as 5∠53 when the radius is already known.
- Compare up to four complex numbers by modulus.
- Use the exact radical output when the decimal value is not the cleanest answer.
Frequently Asked Questions
Sources and References
- Complex ModulusWolfram MathWorld
- Complex NumbersOpenStax
- Complex Number Conversion: Rectangular and Polar FormsCalculators Math
Calculations are based on the listed reference sources. Links open in a new tab.
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