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:::<math> = \left({ac + bd \over c^2 + d^2}\right) + i\left( {bc - ad \over c^2 + d^2} \right). </math>
=== Square roots ===
Each complex number has two square roots.
Consider
:<math>z=a+bi \ </math>
where
:<math>r=\sqrt{a^2+b^2}</math>
and
:<math> \phi = \arctan \left ( \frac b a \right )</math>.
The quadrant of <math>\phi \ </math> is determined by the signs of ''a'' and ''b''.
The square roots are
:<math>\pm\sqrt{\frac{r+a} 2 } \ \pm\ i \ \sqrt{\frac{r-a} 2}</math>
where the signs match if
:<math>0< \phi<\pi \ </math>,
but are different, if not.
===Matrix representation of complex numbers===
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