I've been working on this equation, here's what I have so far:
$\displaystyle z^2-4z+26=0$
$\displaystyle z^2-4z+4=30$
$\displaystyle (z-2)^2=30$
$\displaystyle z-2= +- Square root of 30$
...
And here I'm lost. Please help.
This is not correct. It has to be:
$\displaystyle z^2-4z+26=0$
$\displaystyle \Leftrigharrox (z^2-4z+4)+22=0$
$\displaystyle \Leftrightarrow (z-2)^2=-22$
$\displaystyle \Lefrightarrow z-2= \pm \sqrt{-22}$
$\displaystyle \Leftrightarrow z=\pm \sqrt{-22} + 2$
Now, what's $\displaystyle \sqrt{-22}$?
Note that $\displaystyle D<0$ therefore there're only complex roots, like we obtained.