I am doing some work with z transforms which are littered with quadratics, but I am slightly confused about a fundamental when solving a quadratics with an imaginary component.

$\displaystyle 2s^2-2s+1 = 0$

$\displaystyle \frac{2\pm\sqrt{-4}} {4} = \frac{2\pm2j} {4} = \frac{1} {2} \pm \frac{1}{2}j $

thats fine. no problem. its next example which has me confused,

$\displaystyle s^2 + 2s + 5 = 0$

$\displaystyle \frac {-2\pm \sqrt{-16}} {10} = \frac {-2 \pm 4j} {10} = -\frac{1}{5} \pm \frac{2}{5}j $

but the answer should be,

$\displaystyle -1 \pm 2j$

so what happens to the denominator?

thanks!