Complex numbers have form a + bi, where i² = −1. Addition/subtraction: combine real and imaginary parts. Multiplication: (a+bi)(c+di) = (ac−bd) + (ad+bc)i. Division: multiply by conjugate. Modulus |z| = √(a²+b²). Polar form: z = r(cos θ + i sin θ) = re^(iθ).
How to Use
Enter two complex numbers:
- Z₁: Real + imaginary parts
- Z₂: Real + imaginary parts
- Results: All operations shown
Operations
- Add: (a+c) + (b+d)i
- Subtract: (a−c) + (b−d)i
- Multiply: (ac−bd) + (ad+bc)i
- Divide: multiply by conjugate/|z|²
Polar Form
z = r·e^(iθ) where r = |z| = √(a²+b²) and θ = atan2(b,a). Multiplication in polar: multiply moduli, add angles. Division: divide moduli, subtract angles.
Step-by-Step Instructions
- 1Enter Z₁ real and imaginary parts.
- 2Enter Z₂ real and imaginary parts.
- 3View all operation results.
- 4Check modulus and argument.
- 5See polar form conversion.