Unformatted text preview: i = √-1. Complex numbers are added according to the rule ( a + bi ) + ( c + di ) = ( a + c ) + ( b + d ) i, and complex numbers are multiplied according to the rule ( a + bi ) · ( c + di ) = ( a-d ) + ( b + c ) i. (Notice that the multiplication is just obtained by FOILing.) Deﬁne an order on the complex numbers by declaring that a + bi ≤ c + di, if a ≤ c AND b ≤ d . Does this turn C into an ordered ﬁeld? Why or why not? Be sure to justify your answers! (You only need to check axioms O1-O4. Don’t worry about showing that C is a ﬁeld.) 1...
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- Fall '10