Hi I have this question that is very easy I am sure but I am having a hard time trying to figure out what the last part is asking! anyways here is the question:

Find the four roots of $\displaystyle z^4 + 4 = 0$ and use them to factor $\displaystyle z^4 + 4$ into the product of two quadratic factors with real coefficients.

Ok I was able to find the 4 roots with ease they are $\displaystyle (1+i), (-1+i), (1-i), (-1-i)$

Now for the part that asks product of two quadratic factors with real coefficients. this is where I

Because I have no idea what they are even asking and my book/teacher expects us to already know this because its so basic... well

My GUESS was $\displaystyle (z^2-2z+2)(z^2+2z+2)$ but I didnt use the roots at all to come to that answer I used some formula I found on web.

So please someone out there make me less dumb.