Online Complex Numbers Calculator
Perform operations on complex numbers a + bi: addition, subtraction, multiplication, division, modulus, and conjugate values.
Complex Numbers Calculator
Arithmetic, polar/trigonometric forms, modulus, argument, and Argand plane visualization
Complex Plane (Argand Diagram)
Operation Result
Forms & Properties of z₁
How to use
- Input real (Re) and imaginary (Im) components of complex number z1.
- Input real and imaginary components of complex number z2.
- Choose operator (+, -, *, /, modulus, conjugate).
- View result in standard algebraic rectangular form along with absolute magnitude.
Calculation Examples
Addition: (2 + 3i) + (1 + 2i) = 3 + 5i.
Subtraction: (5 + 4i) - (2 + i) = 3 + 3i.
Multiplication: (1 + i) * (2 + i) = 1 + 3i (since i² = -1).
Modulus: |3 + 4i| = √(3² + 4²) = 5.
Calculation Methodology
Calculations adhere to complex field algebra using i² = -1. Complex modulus represents Euclidean distance from the origin on the Argand plane.
Frequently Asked Questions
What is a complex number?
A number of the form a + bi consisting of real part a and imaginary part b, with imaginary unit i = √(-1).
Which operations are supported?
Addition, subtraction, multiplication, division, complex conjugate, and modulus evaluation.
What is the modulus of a complex number?
The modulus |z| = √(a² + b²) denotes vector distance from the origin on the complex plane.
How is division handled?
By multiplying numerator and denominator by the complex conjugate of the divisor.
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