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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