Complex Multiplication Calculator

Use our free complex multiplication calculator to multiply two complex numbers (a+bi) × (c+di) using FOIL with a detailed step-by-step breakdown.

Math

z₁ =

z₂ =

Formula

Multiply two complex numbers using the FOIL method with full breakdown. Also shows the modulus property |z₁·z₂| = |z₁|·|z₂|.

(a₁+b₁i) × (a₂+b₂i) = (a₁a₂−b₁b₂) + (a₁b₂+b₁a₂)i

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter z₁ as a+bi.
2Enter z₂ as c+di.
3Click Calculate to see the product and breakdown.

Examples

(3+4i)×(1+2i)

1.(3·1−4·2)+(3·2+4·1)i
2.=(3−8)+(6+4)i=−5+10i

Result: 11.1803398875

(2+i)(2−i)

1.(2·2−1·(−1))+(2·(−1)+1·2)i=(4+1)+(−2+2)i=5

Result: 5

Frequently Asked Questions

Use FOIL: (a+bi)(c+di)=ac+adi+bci+bdi² = (ac−bd)+(ad+bc)i (since i²=−1).

|z₁·z₂| = |z₁|·|z₂| — the modulus of the product equals the product of the moduli.

(a+bi)(a−bi)=a²+b² which is purely real.

Related Calculators

Complex Number Calculator Complex Division Calculator Complex Addition Calculator Polar Form Calculator Percentage Calculator Basic Calculator

CalculateMe Team

Last updated: 2026-07-15

Complex Multiplication Calculator

Formula

How It Works

Examples

(3+4i)×(1+2i)

(2+i)(2−i)

Frequently Asked Questions

How do you multiply complex numbers?

What is the product modulus?

What happens with conjugates?

Related Calculators

Complex Multiplication Calculator

Formula

How It Works

Examples

(3+4i)×(1+2i)

(2+i)(2−i)

Frequently Asked Questions

How do you multiply complex numbers?

What is the product modulus?

What happens with conjugates?

Related Calculators