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Homework Statement
Let K be the closure of Qu{i}, that is, K is the set of all numbers that can be obtained by (repeatedly)
adding and multiplying rational numbers and i, where i is the complex square root of 1.
Show that K is a Field.
Homework Equations
The Attempt at a Solution
I am having trouble starting on this problem:
What I know:
Proof the Zero vector is in the set
Proof both addition and scalar multiplication
proof additive and multiplicative inverse
^ am I missing anything?
And i am guessing I have to prove it in the form of
let Q be rational numbers
and scalars a and b in F (field)
aQ + bi = K