Complex Number Calculator

Overview

Complex Number Calculator handles common and advanced complex operations, including arithmetic, polar and exponential form display, plus conjugate, square root, reciprocal, and square outputs.

Key Features

• Compute add, subtract, multiply, and divide for Complex A and Complex B.
• Show modulus, argument, and exponential form in real time.
• Provide conjugate, square root, reciprocal, and square for each input complex number.
• Display result in algebraic form with separate real and imaginary parts.

How to Use

1. Enter real and imaginary parts for Complex A and Complex B.
2. Click an operation button: add, subtract, multiply, or divide.
3. Check the result panel for algebraic form and components.
4. Review modulus, argument, and exponential form in the polar panel.
5. Review conjugate, square root, reciprocal, and square in the single-calculation panel.

Formula Notes

• Addition: (a + bi) + (c + di) = (a + c) + (b + d)i
• Subtraction: (a + bi) - (c + di) = (a - c) + (b - d)i
• Multiplication: (a + bi) × (c + di) = (ac - bd) + (ad + bc)i
• Division: (a + bi) ÷ (c + di) = [(ac + bd) + (bc - ad)i] / (c² + d²)
• Modulus: |z| = √(a² + b²)
• Argument: arg(z) = arctan(b / a)

Use Cases

• Complex analysis, linear algebra, and signal-system learning.
• AC circuit impedance and phase calculations.
• Engineering modeling in control, communication, and algorithm analysis.

Notes

• Division is unavailable when Complex B equals zero.
• Reciprocal is unavailable when the complex number equals zero.
• All computations run locally in your browser.