In the complex plane , there are three cube roots of one. Let zeta be the cube root of one which has positive imaginary part. Show that zeta is a quadratic integer in Q[sqrt(-3)] by writing it in the form (a+bsqrt(-3))/2 , where a and b are rational integers and a and b are either both even or both odd. Then write it in the form m+n*((1+sqrt(-3))/2), where m and n are rational integers.
I have totally no idea what the questions about.
Could you please give me detail explaination if you can solve them? Thank you very much.
Note : I have deleted Question 2 . Since no one reply for it and I have just solved it.