Our CBSE Notes for Introduction Class 11 maths 5. Complex Number and Quadratic Equations - CBSE Notes - Toppers Study is the best material for English Medium students cbse board and other state boards students.

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

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

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- All Chapter review quick revision notes for chapter 5. Complex Number and Quadratic Equations Class 11
- NCERT Solutions And Textual questions Answers Class 11 Mathematics
- Extra NCERT Book questions Answers Class 11 Mathematics
- Importatnt key points with additional Assignment and questions bank solved.

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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
- Class 11 Ncert Solutions
- Solution Chapter 5. Complex Number And Quadratic Equations Class 11
- Solutions Class 11
- Chapter 5. Complex Number And Quadratic Equations Introduction Class 11

## 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

*x ^{2} + 3x + 5 = 0*

*a = 1, b = 3, c= 5 *

*D = *

* = 3 ^{2}– 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

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

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