Complex Number Calculator

Addition & Subtraction

Add or subtract the real and imaginary parts separately:

• (a + bi) + (c + di) = (a+c) + (b+d)i
• (a + bi) − (c + di) = (a−c) + (b−d)i

Example: (3 + 2i) + (1 + 4i) = 4 + 6i

Multiplication & Division

Multiplication: Use FOIL method

• (a + bi)(c + di) = (ac−bd) + (ad+bc)i

Division: Multiply by conjugate

• (a + bi) ÷ (c + di) = [(a + bi)(c − di)] / (c² + d²)

Rectangular Form

Standard form: a + bi

• a = real part
• b = imaginary part
• i = √(−1), where i² = −1

Polar Form

Polar form: r(cos θ + i sin θ)

• r = magnitude = √(a² + b²)
• θ = angle = arctan(b/a)
• Also written as: r∠θ or r·e^(iθ)