🔢 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)