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Complex Number Calculators

Complex Division Calculator

Divide complex numbers by multiplying by the conjugate of the denominator; result in a + bi and polar form.

Enter values

Results update as you type.

Result

z₁ ÷ z₂

-1 + 2i

Polar form
2.23606798 ∠ 116.565051°
Modulus |z|
2.23606798

About the Complex Division Calculator

Divide complex numbers by multiplying by the conjugate of the denominator; result in a + bi and polar form.

Also known as: divide complex numbers, complex quotient.

How to use this calculator

  1. Enter z₁, z₂.
  2. The result updates instantly as you type — press Calculate (or Enter) at any time.
  3. Review the breakdown shown under the main result.
  4. Use Copy result or Share to save the answer or send a link with your inputs.

Formula

(a + bi)/(c + di) = [(ac + bd) + (bc − ad)i] / (c² + d²)

Worked example

Using the values pre-filled in the calculator above:

  • z₁: 3 + 4i
  • z₂: 1 - 2i

the calculator returns:

  • z₁ ÷ z₂: -1 + 2i
  • Polar form: 2.23606798 ∠ 116.565051°
  • Modulus |z|: 2.23606798