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Complex Numbers Calculator

Perform addition, subtraction, multiplication, division, and convert between rectangular and polar forms. Visualize results instantly on the Argand diagram.

Operations

Polar & Rectangular

Argand Plot

Complex Numbers Calculator

Z1

Magnitude: 3.606, Angle: 33.69°

Z2

Magnitude: 4.123, Angle: -75.96°

Result

0.000 + 0.000i

Argand Diagram

Complex Numbers Calculator

Our powerful online complex numbers calculator simplifies complex number arithmetic for students, engineers, and mathematicians. Easily perform addition, subtraction, multiplication, and division of two complex numbers. Use the tool to convert between rectangular and polar forms and visualize your results instantly on the interactive Argand diagram.

How to Use This Calculator

1. Basic Operations

Enter the real and imaginary parts for Z₁ and Z₂ in their fields. Select an operation (+, -, *, /) and get an instant result and step-by-step breakdown.

2. Form Conversions

The calculator displays the magnitude and angle automatically. Use the `Rect → Polar` or `Polar → Rect` buttons for quick conversions between forms.

3. Argand Diagram

Visualize your complex numbers and the result of your operation on a real-time plot. This helps you understand the geometric representation of the numbers.

Applications of Complex Numbers

  • Electrical Engineering: Used to analyze alternating current (AC) circuits, where they simplify the representation of phase relationships between voltage and current.
  • Signal Processing: Complex Fourier transforms are used to decompose signals into their constituent frequencies, a fundamental operation in audio and image processing.
  • Quantum Mechanics: The wave function of a particle is a complex-valued function, and complex numbers are indispensable for describing quantum phenomena.
  • Fluid Dynamics: Complex numbers are used to model potential flow around objects and in analyzing two-dimensional fluid flow.

Frequently Asked Questions

What is a Complex Number?
How do I perform basic operations?
What are Rectangular and Polar forms?
What is an Argand Diagram?