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
- Enter real and imaginary parts for Complex A and Complex B.
- Click an operation button: add, subtract, multiply, or divide.
- Check the result panel for algebraic form and components.
- Review modulus, argument, and exponential form in the polar panel.
- 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.