Complex Number Multiplication Visualizer
First Complex Number (z₁)
+
i
Second Complex Number (z₂)
+
i
Numerical Results
Graphical Visualization
z₁ = a + bi
z₂ = c + di
z₁ × z₂
Multiplication Formulas
Rectangular Form: (a + bi)(c + di) = (ac - bd) + (ad + bc)i
Polar Form: r₁e^(iθ₁) × r₂e^(iθ₂) = (r₁ × r₂)e^(i(θ₁ + θ₂))
Magnitudes multiply: |z₁ × z₂| = |z₁| × |z₂|
Arguments add: arg(z₁ × z₂) = arg(z₁) + arg(z₂)