I've been asked to find out if some field extensisons are normal. I want to know if I'm thinking about these in the right way. For Q(a):Q I first find the minimal polynomial for a in Q[a]. Then I look at all zeros of that polynomial. If all of the zeros are in Q(a) the extension is normal. Example: Q(1+i):Q 1+i = x -1 = x^2-2x+1 x^2-2x+2 is irreducible over Q and the minimal polynomial of 1+i. the zereos are: 1+i, 1-i they are both in Q(1+i) so this is a normal extension. Correct?