91Ó°ÊÓ

Show that the set of all complex numbers \(a+b i\), with \(a\) and \(b\) rational, satisfies all the axioms for a field.

Is it possible to make addition and multiplication tables so that the four elements \(0,1,2,3\) form the elements of a field? Prove your statement. [Hint: In the multiplication table each row, other than the one consisting of zeros, must contain the symbols \(0,1,2,3\) in some order.]

Express each given combination of intervals as an interval. Plot a graph in each case. $$ (-\infty, 2) \cap(-\infty, 4) $$

Find the solution set of the given inequality. $$ x /(2-x)<2 $$

Using the theorems of this section show: (i) If \(a>b>0\) and \(c>d>0\), then \(a \cdot c>b \cdot d\). (ii) If \(ab \cdot d\).