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Introduction class 11 Mathematics Chapter 5. Complex Number and Quadratic Equations

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Introduction Class 11 Maths 5. Complex Number And Quadratic Equations - CBSE Notes - Toppers Study
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5. Complex Number and Quadratic Equations

| Introduction |

Introduction Class 11 maths 5. Complex Number and Quadratic Equations - CBSE Notes - Toppers Study

Introduction

⇒

First we know about the real number;

π√

Real Number includes;

(i) Whole numbers: like 0, 1, 2, 3, 4.................................. etc.

(ii) Rational numbers: like 4/5, 0/6, 0.333........, etc.

(iii) irrational numbers: like π, √3, √2 etc.

We have learnt quadratic equation in previous class. The nature of quadratic equations is

D > 0, {Real and unequal roots}

D = 0, {Real and equal roots}

D < 0, {No Real roots, i.e. Imaginary root}

Look the following example

x² + 3x + 5 = 0

a = 1, b = 3, c= 5

D =

= 3²– 4 ×1 × 5

= 9 – 20

= –11

D < 0, {so equation has no real but imaginary roots}

Now we have to find the roots

Here both the value of x is an imaginary number, which is made by the composition of (i), symbol “i” is called iota. Such number is called complex number.

1. Imaginary Number: A number whose square is negative is known as an imaginary number.

Ex: , , , etc.

2. Complex number: Any number which is of the form of x + iy, where x and y are real number and i = is called a complex number.

Ex : 3 + i5, 2 – i3, 5 + i2 and 4 +i3 etc.

It is denoted by z i.e. z = x +iy, in which Re(z) = x and Im(z) = y

A complex number has two parts;

(I) real part Re(z) {∈ R}

real part : 2, 3, 5, and 4 or may be any real number.

(II) imaginary part Im(z) {Real number with i(iota)}

imaginary part: i, i2, i3, i4, and i5 etc.

Every Real number is a complex number if x∈ R and y ∈ R; such as

z = 3 ⇒ 3 +i0, x = 3, y =0

z = –3⇒ – 3 +i0, x = –3, y =0

z = 7 ⇒ 7 +i0, x = 7, y =0

3. See the following complex numbers

z = 3, z = i3, z = 4, z = i7

z = 3 and z = 4 are purely Real

z = i3 and z = i7 are purely Imaginary

Other Pages of this Chapter: 5. Complex Number and Quadratic Equations

1. Chapter 5. Complex Number and Quadratic Equations | Introduction

2. Chapter 5. Complex Number and Quadratic Equations | Complex Number

3. Chapter 5. Complex Number and Quadratic Equations | Algebra of Complex Numbers

4. Chapter 5. Complex Number and Quadratic Equations | The Modulus and Congugate of a Complex Number

5. Chapter 5. Complex Number and Quadratic Equations | Polar representation of a complex number

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