Let , then is one of the primitive m th roots of unity.
a) Show that if m|n.
Let mt = n for some integer t.
Pick an element , with a and b rational numbers.
Then it equals to Now, is this element in ? I just don't know if is a rational number.
b) Show that .
There is a theorem that state: Let be a primitive pth root of unity, p an odd prime. if
Now, is a primitive pth roof of unity?