🔢 Complex Number Calculator
Perform arithmetic operations with complex numbers. Convert between rectangular (a + bi) and polar (r∠θ) forms.
z₁ = a + bi
z₂ = c + di
Rectangular Form (a + bi)
Polar Form (r∠θ)
Complex Number Operations
Forms
Rectangular: z = a + bi
Polar: z = r(cos θ + i sin θ) = r∠θ
Exponential: z = re^(iθ)
Operations
| 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) |
Conversions
Rectangular to Polar: r = √(a²+b²), θ = atan2(b,a)
Polar to Rectangular: a = r·cos(θ), b = r·sin(θ)