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Milica
Milica asked in Science & MathematicsMathematics · 9 years ago

Consider the set Q[i] of numbers a+bi where a and b are in Q. Show that Q[i] is a field.?

I need help with this, please..

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  • Anonymous
    9 years ago
    Favorite Answer

    I happen to be working on that problem right now, and I don't know that this is an actual answer, but it's what I put. I don't know if each property needs to be proven, but here's the one for inverses.

    For any a in F (field), there exists an element b in F such that a*b=b*a=1

    assume (a+bi)X=1 X in F

    (a+bi)X=1

    X=1/(a+bi)

    X=1/(a+bi) * (a-bi)/(a-bi)

    X=(a-bi)/a^2+b^2

    X=a/a^2+b^2 - bi/a^2+b^2

    I don't know if all of the properties of rings need to be proven, but if so, I have no clue how.

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