Show that {Q(√13,+,*} is a field?
Let Q(√13 ={x+y√13 where x,y are elements of Q}
Q of course is rational numbers
Addition and multiplication are defined as follows
(a+b√13)+(c+d√13) =(a+c)+(b+d)√13
(a+b√13)(c+d√13) = (ac+13bd)+(ad+bc)√13
Show that {Q(√13,+,*} is a field