Question: How can I force Maple to be smarter about roots of unity

Say I define the following variables.

These are all nineth roots of unity. An equivalent definition would be:

In fact, the following code shows that aa[i] /a[i] =1 for all i, so one would concluse aa[i]=a[i]:

for i to 9 do 
simplify(a[i]/aa[i])
end do

But when I try to check via "Equal":

I get as output

                              true
                             false
                             false
                             false
                             false
                             false
                              true
                             false
                             false
The problem goes even further since one representation is accepted as a solution of a linear equation system while the other is not.

Another curiosity:

gives just the same expression, whereas simplifying the same expression to the third power gives 0.