Divide Complex Numbers - Calculator

An easy to use calculator that divides two complex numbers.

Let \( w \) and \( z \) be two complex numbers such that \( w = a + ib \) and \( z = A + iB \). The division of \( w \) by \( z \) is based on multiplying numerator and denominator by the complex conjugate of the denominator:

\( \dfrac{w}{z} = \dfrac{a + ib}{A + iB} \)
Multiply numerator and denominator by the conjugate of the denominator
\( = \dfrac {(a + ib)(A - iB)} { (A + iB)(A - iB)} \)
Expand the numeartor and the denominator
\( = \dfrac { a A + b B + i(b A - a B) } { A^2 + B^2} \)
Write in standard form
\[ \dfrac{w}{z} = \dfrac{ a A + b B}{A^2 + B^2} + i \dfrac{b A - a B}{A^2 + B^2} \]

Calculadora de división de números complejos

Enter the real and imaginary parts (such as a whole number, decimal, or fraction) of two complex numbers z and w and press "Divide."