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Complex Number Calculator
Perform operations with complex numbers and convert between forms
Complex Number Operations
Complex Number A
Complex Number B
How to Use the Complex Number Calculator
Complex Number Forms
- Rectangular: z = a + bi (real + imaginary parts)
- Polar: z = r∠θ (magnitude and angle)
- Exponential: z = re^(iθ) (using Euler's formula)
Basic Operations
- Addition: (a + bi) + (c + di) = (a + c) + (b + d)i
- Multiplication: (a + bi)(c + di) = (ac - bd) + (ad + bc)i
- Division: Multiply by conjugate of denominator
- Conjugate: z* = a - bi (flip sign of imaginary part)
Properties and Relationships
- Magnitude: |z| = √(a² + b²)
- Argument: arg(z) = arctan(b/a)
- De Moivre's Theorem: z^n = r^n(cos(nθ) + i sin(nθ))
- Euler's Formula: e^(iθ) = cos(θ) + i sin(θ)
Applications
- Engineering: AC circuit analysis, signal processing
- Physics: Quantum mechanics, wave functions
- Mathematics: Polynomial roots, Fourier analysis
- Computer Graphics: Rotations and transformations
Related Calculators
- Algebra Solver - For polynomial equations with complex roots
- Trigonometric Calculator - For angle calculations in polar form
- Vector Calculator - For 2D vector operations similar to complex numbers
- Matrix Calculator - For linear transformations in complex plane