Factored $z^4 + 4$ into $(z^2 - 2i)(z^2 + 2i)$. How to factor complex polynomials such as $z^2 - 2i$ and $z^2 + 2i$? I was wondering how to factor complex polynomials such as  $z^2 - 2i$ and $z^2 + 2i$?
I originally had $z^4 + 4$, which I factored to $(z^2 - 2i)(z^2 + 2i)$ by substituting $X = z^2$ and using the quadratic formula. However, I'm not sure if there exists any method to factor $z^2 - 2i$ and $z^2 + 2i$? 
I would greatly appreciate it if people could please explain how one would go about this.

Using difference of squares ...
$$z^2-2i= z^2  - 2e^{i \frac \pi 2} = z^2 - (\sqrt 2 e^{i \frac \pi 4})^2
\\ = (z+\sqrt 2 e^{i \frac \pi 4})(z-\sqrt 2 e^{i \frac \pi 4})$$
$$z^2+2i= z^2  - 2e^{i \frac {3\pi} 2} = z^2 - (\sqrt 2 e^{i \frac {3\pi} 4})^2
\\ = (z+\sqrt 2 e^{i \frac {3\pi} 4})(z-\sqrt 2 e^{i \frac {3\pi}4})$$
