# roots of i, polynomial

• Feb 28th 2011, 04:10 AM
gpenguin
roots of i, polynomial
Let alpha and -alpha be the square roots of i.
Write down a degree two polynomial having alpha and -alpha as its roots. Then write down a degree four polynomial with integer coefficients having alpha and negative alpha among its roots. What are the other two roots of this polynomial.

I don't know if I can't do this because I really don't understand what the question is asking me or if the question is just going straight over my head :(
• Feb 28th 2011, 04:13 AM
Prove It
What about $\displaystyle f(z) = (z - \alpha)(z + \alpha)$?
• Feb 28th 2011, 04:51 AM
gpenguin
I'm really sorry. I still don't get where to go.
• Feb 28th 2011, 06:08 AM
Plato
The value $\alpha=\cos\left(\frac{\pi}{4}\right)+i~\sin\left( \frac{\pi}{4}\right)$, that is one square root of $\mathif{i}$.
Is $\alpha$ a root of $z^4+1=0~?$
What are the other roots?