This chapter will enable you to learn the concepts and application of:
N is closed for addition and multiplication. The solution of x + 5 = 3 is not contained in N but in Z.
Solution of 5x = 3 is not contained in Z but in Q.
Q does not cover the number line completely, R does.
Solution of x2 = 2 is not contained in Q but in R.
Solution of x2 + 1 = 0 is not contained in R but in C.
(∵ C is a field)
If for the numbers (a, b) and (c, d) of R × R, equality, addition and multiplication are defined as under then R × R is known as the set of complex numbers C.
Equality: (a,b) = (c,d) ⇔ a = c ;