So put a=1 and b=omega
So the expression becomes:
and using the roots of unity formula in my previous post
As omega can only take one of two values, it looks to me like the expression can only take one of two values.
Bob
]]>I think that's a suitable starting point, but I'll have to have a longer think about how the combinations affect that. I'd expect that the answer will depend on whether n has the form 3k, or 3k+1, or 3k+2.
Hopefully back later.
Bob
]]>Your Latex has an error so we're not seeing this question correctly.
After the 'e' you have a ^ and then a complicated expression. Powers will only display correctly if a single character follows or the power is enclosed in {} brackets. I have tried putting in a pair and get this:
If n is a positive integer and
is a cube root of unity, then find the number of possible values ofIs that what you intended? And is the 'matrix' just to get k combinations from n ?
Bob
]]>Since omega is a cube root of unity, omega ^ 3 = 1. Therefore omega^n takes up to 3 values: omega, omega^2 (or 1/omega) and omega^3=1.
Since omega is not 1, omega, omega^2 and omega^3 have three distinct values, so there are exactly 3 values.
]]>