I never ever EVER want to take that test again. Fortunately, the problems weren't terrible this time around, but 6 hours is still a ridiculous amount of time to be taking a test
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Fair enough. I suppose I meant a formulation which uses the standard multiplication rule on R^2, rather than the complex one. Of course, at some level the same multiplicative structure needs to be in there, but I'm envisioning this at the level of, say, a pair of coupled equations.
well, there is no standard multiplication rule for R^2.
but you can easily get the 'pair of coupled equations' that you want. just write out everything explicitly, writing each complex variable z as a+bi. Then separate each equation into its real part and its imaginary part. Then remove the i's. Presto.
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Well, why not? Usually we define C as being a field consisting of the set R^2 and the multiplication rule (0,1)*(0,1)=(-1,0)... eh? right?
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but you can easily get the 'pair of coupled equations' that you want. just write out everything explicitly, writing each complex variable z as a+bi. Then separate each equation into its real part and its imaginary part. Then remove the i's. Presto.
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