# 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."

 w = -1 + i -9 z = 1/2 + i 2.1 $\dfrac{w}{z} =$ + i (Exact value) $\dfrac{w}{z} =$ + i (approximate value)
More Math Calculators and Solvers .
Operations on Complex Numbers in Polar Form

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