Complex Division Calculator

Use our free complex division calculator to divide two complex numbers (a+bi) ÷ (c+di) using the conjugate method with a detailed step-by-step breakdown.

Math

z₁ =

z₂ =

Formula

Divide two complex numbers using the conjugate method — multiply numerator and denominator by the conjugate of the denominator, then simplify. Full step-by-step breakdown.

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

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 (numerator).
2Enter z₂ as c+di (denominator, cannot be zero).
3Click Calculate to see the quotient and breakdown.

Examples

(3+4i)÷(1+2i)

1.Multiply by conjugate 1−2i
2.Numerator: (3+4i)(1−2i)=11−2i
3.Denominator: 1²+2²=5
4.Result: (11/5)−(2/5)i=2.2−0.4i

Result: 2.2360679775

(1+i)÷(1−i)

1.(1+i)/(1−i) = i

Result: 1

Frequently Asked Questions

Multiply numerator and denominator by the conjugate of the denominator, then simplify using i²=−1.

Division by zero is undefined and will show an error.

(a+bi)/(c+di) = (a+bi)(c−di)/(c²+d²) — rationalizes the denominator.

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CalculateMe Team

Last updated: 2026-07-15

Complex Division Calculator

Formula

How It Works

Examples

(3+4i)÷(1+2i)

(1+i)÷(1−i)

Frequently Asked Questions

How do you divide complex numbers?

What if the denominator is zero?

What is the conjugate method?

Related Calculators

Complex Division Calculator

Formula

How It Works

Examples

(3+4i)÷(1+2i)

(1+i)÷(1−i)

Frequently Asked Questions

How do you divide complex numbers?

What if the denominator is zero?

What is the conjugate method?

Related Calculators