Let \(\omega\) be a complex number such that \(\omega^7 = 1\) and \(\omega \neq 1\). Let \(\alpha = \omega + \omega^2 + \omega^4\) and \(\beta = \omega^3 + \omega^5 + \omega^6\). Then \(\alpha\) and \(\beta\)
are roots of the quadratic x^2 + px + q = 0 for some integers p and q. Find p and q.
Here's an interesting problem I've been stumped on, any pointers and help? Thanks!
Could you tell me how you get from the last but one line to the last one, (without the use of a calculator). ?
I cheated and used a calculator (well, Mathcad's calculation facilities).