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1. Let S be the set of all nonzero real numbers. That is, S = R - {0}. Consider the relation R on S given by xRy iff xy > 0.
(a) Prove that R is an equivalence relation on S, and describe the distinct equivalence classes of R.
(b) Why is the relation R2 on S given by xR2y iff xy < 0 NOT an equivalence relation?
Now we have to discuss the basic operations for complex numbers. We'll begin with addition & subtraction. The simplest way to think of adding and/or subtracting complex numbers is
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