# A calculus of the absurd

##### 15.1.2 Dividing complex numbers

Another operation we can perform is division. To divide two complex numbers (which we can call $$w$$ and $$z$$), we do something similar to rationalising the denominator (except for complex numbers).

For example, in the specific case where $$z = 1 + i$$ and $$w = 3 + 4i$$, we have can make the denominator "real" through multiplication by the complex conjugate.

\begin{align} \frac {z}{w} &= \frac {1 + i}{3 + 4i} \\ &= \frac {1 + i}{3 + 4i} \cdot \frac {1+i}{3 - 4i} \\ &= \frac {(1+i)(3-4i)}{25} \end{align}