Complex Number Calculator

Perform operations, explore properties, and convert between rectangular and polar forms of complex numbers.

Complex Numbers
Grade 9+
Intermediate

Features

  • Addition, subtraction, multiplication, division of complex numbers
  • Calculate modulus, argument, and conjugate
  • Convert between rectangular and polar forms
  • Tabs for operations, properties, and conversion
  • Real-time result display
  • Input validation and error handling

First Complex Number

Second Complex Number

About Complex Numbers

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, satisfying i² = -1.

Key Concepts

  • Rectangular form: a + bi (where a is the real part and b is the imaginary part)
  • Polar form: r∠θ (where r is the modulus and θ is the argument)
  • Modulus: |a + bi| = √(a² + b²)
  • Argument: θ = tan⁻¹(b/a)
  • Conjugate: (a + bi)* = a - bi

Complex numbers are essential in many fields including electrical engineering, quantum physics, signal processing, and control theory.