When am I done solving complex quadratic equations?

Below is a complex quadratic equation I think I have solved.

$z^2-2z+i=0$ gives $z=\frac{2\pm\sqrt{4-4i}}{2}$. This becomes $z=1\pm\sqrt{1-i}$ with some basic algebra.

My question is: am I done here? In prior problems I had to evaluate expressions such as $\sqrt{i-1}$ to find it equivalent to $\sqrt[4]{2}*\operatorname{cis}(3\pi/8)$ and $\sqrt[4]{2}*\operatorname{cis}(11\pi/8)$. Hopefully this question is not as rudimentary as I suspect it to be!