Answer with explanation please. Thanks
Let \(\omega\) be a nonreal root of \(z^3 = 1.\) Find the number of ordered pairs \((a,b)\) of integers such that \(|a \omega + b| = 1.\)
There are four pairs that work: (1,0), (-1,0), (0,1), (0,-1).
They are the only ones I can think of too.
I got down to
\(a^2+b^2 -ab=1\)
Not sure how to determine if those are the only 4 answers.
The following also work:
\(a=\frac{2}{\sqrt3}, b=\frac{1}{\sqrt3}\\a=-\frac{2}{\sqrt3}, b = -\frac{1}{\sqrt3}\)
How did you come up with those Alan?
Is there some technique you can show us?
+140 
