Here is a problem that I'm having some trouble solving.
"In the complex plane, there exists three cube roots of one. Let X be the cube root of one which has positive imaginary part. Knowing this, it can be shown that X is a quadratic integer in Q[Sqrt(-3)] written in the form of (a+b*Sqrt(-3))/2 where a and be are either both even or both odd and are rational. Once written in this form, it can be written in the form: m+[(n/2)(1+Sqrt(-3))].
On a complex plane, how can one represent the quadratic integers in Q[Sqrt(-1)], Q[Sqrt(-3)], and Q[Sqrt(-5)]? I specifically need to note the points 0, 1, and sqrt(d) and which points are "units".
Any and all help is greatly appreciated