Let C denote the set of complex numbers, with the usual addition (+) and multiplication (×) operations.
Which of the following are true? If false, indicate what property does not hold.
(C,+) is a group
(C,×) is a group
(C-{0},+) is a group
(C-{0},×) is a group
(C,+,×) is a ring
(C,+,×) is a commutative ring with identity
(C,+,×) is a field
Let Q(√ 2 ) =
{ a + b*√ 2 | a and b are
in Q}. Show that this set, with the usual addition and multiplication, is a field.