Business Mathematics

4

Complex Numbers

LEARNING OBJECTIVES

This chapter will enable you to learn the concepts and application of:

• What is Complex number.
• Advance application of complex number

INTRODUCTION

Remember

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)

SET OF COMPLEX NUMBERS IN C

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 ;