Complex_number - CHAPTER 3 COMPLEX NUMBER 3.1 INTRODUCTION...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CHAPTER 3 COMPLEX NUMBER 3.1 INTRODUCTION Lets a quadratic equation be in the form of 2 = + + c bz az ( 1 ) The usual method to find the roots from this equation is by using formula a ac b b z 2 4 2- - = If 4 2 <- ac b , then the solution of z is in term of square root of negative number y x z 1- = If 1- is written as i then the solution become iy x z + = and iy x z- = ( 2 ) Equation (2) are known as Complex Number , composed of a real part x and an imaginary part iy . Complex number has its conjugate , the only difference between them is the sign of the imaginary part, that is iy x z- = is the conjugate of iy x z + = , and vise versa. We denoted the conjugate as z . 3.2 OPERATIONS Operation of addition, subtraction, multiplication and division are also can be performed on complex number as usual together with the rule that 1 2- = i . Example 1: Let i z 5 2 1 + = and i z 2 1 2 +- = , find (a) 2 1 z z + (b) 2 1 z z- (c) 2 1 z z (d) 2 1 z z Documents PDF Complete Click Here & Upgrade Expanded Features Unlimited Pages Solution (a) ( 29 ( 29 i i i z z 7 1 2 1 5 2 2 1 + = +- + + = + (b) ( 29 ( 29 i i i z z 3 3 2 1 5 2 2 1 + = +-- + =- (c) ( 29 ( 29 i i i i i i i z z-- =--- = +- +- = +- + = 12 10 2 10 5 4 2 2 1 5 2 2 2 1 (d) ( 29 ( 29 ( 29 ( 29 i i i i i i i i i i i z z 5 9 5 8 5 9 8 4 1 10 9 2 2 1 2 1 2 1 5 2 2 1 5 2 2 2 2 1- =- =---- =-- +--- + = +- + = In example 1 (d), for division of complex number, we convert the complex number in the denominator into real number, by multiplying both numerator and denominator by the conjugate of the denominator. 3.3 THE ARGAND DIAGRAM We will present complex number graphically on Cartesian co-ordinate system and Polar co-ordinate system. 3.3.1 CARTESIAN FORM Let iy x z + = 1 , the graph using Cartesian coordinate system is as figure below. iy iy x z + = 1 iy x x In Cartesian coordinate system, x-axis represented real part while y-axis represented imaginary parts of complex number. The addition and subtraction also can be shown graphically. Documents PDF Complete Click Here & Upgrade Expanded Features Unlimited Pages Let 1 1 1 iy x z + = and 2 2 2 iy x z + = , the graph of 2 1 z z + is as figure below. iy ( 29 2 1 2 1 2 1 y y i x x z z + + + = + 1 z ( 29 2 1 y y i + 2 z x 2 1 x x + 3.3.2 POLAR OR TRIGONOMETRIC FORM Consider the following figure iy ) , ( r r iy x x ) , ( r is the polar coordinate for z , r is the modulus of z and is written as z and is called the argument of z. If iy x z + = , from graph we conclude = cos r x = sin r y Thus...
View Full Document

This note was uploaded on 12/01/2010 for the course SUKAN md taught by Professor Saipon during the Spring '10 term at Albany College of Pharmacy and Health Sciences.

Page1 / 11

Complex_number - CHAPTER 3 COMPLEX NUMBER 3.1 INTRODUCTION...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online