if I define The plane: ##F = ℝ## x ##ℝ = \{ (a, b) | a, b ∈ ℝ \} ##(adsbygoogle = window.adsbygoogle || []).push({});

and define addition and multiplication as:

(a, b) + (c, d) := (a + c, b + d)

(a, b) · (c, d) := (ac, bd)

Then ##F## is a field. right?

would the multiplication as described here make ℂ a field?

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# Field if I define The plane

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