NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations

 

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations: In the earlier classes we have studied that for x2+3=0, x2=-3 and we say that the equation has no real solution. In NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations, we will study how to solve equations like x2+3=0. The NCERT Solutions for Class 11 of this chapter starts with the concept of i (iota), i=\sqrt{-1} and using this we will solve the quadratic equation ax^2+bx+c=0 with b^2-4ac<0. The concept of complex numbers will be used in solving quadratic equations, in solving the alternating current circuits, in vector analysis, etc. 

The main topics of the NCERT Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations are

5.1 Introduction

5.2 Complex Numbers

5.3 Algebra of Complex Numbers

5.4 The Modulus and the Conjugate of a Complex Number

5.5 Argand Plane and Polar Representation

5.6 Quadratic Equations

As mentioned in the first paragraph i=\sqrt{-1} and

\\i^2={-1}\\i^3=-1\times i=-i\\i^4=-1\times-1=1

and any number can be represented as a complex number of the form a+ ib where a is the real part and b is the imaginary part, for example, 1=1+0i. A complex number a+ib in the X-Y plane is represented as follows

is

where 

\\r=\sqrt{a^2+b^2}\\a=rcos\theta\\b=rsin\theta

So a complex number of the form a+ ib can be represented as

 r(cos\theta +i sin\theta)

and the above representation is known as the polar form of a complex number. Practicing all the NCERT Solutions are mandatory for the exam.

The NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations is given below:

NCERT Solutions for Class 11 Mathematics- Chapter-wise

Chapter-1

Sets

Chapter-2

Relations and Functions

Chapter-3

Trigonometric Functions

Chapter-4

Principle of Mathematical Induction

Chapter-6

Linear Inequalities

Chapter-7

Permutation and Combinations

Chapter-8

Binomial Theorem

Chapter-9

Sequences and Series

Chapter-10

Straight Lines

Chapter-11

Conic Section

Chapter-12

Introduction to Three Dimensional Geometry

Chapter-13

Limits and Derivatives

Chapter-14

Mathematical Reasoning

Chapter-15

Statistics

Chapter-16

Probability

NCERT Solutions for Class 11- Subject wise

NCERT Solutions for Class 11 Biology

NCERT Solutions for Class 11 Maths

NCERT Solutions for Class 11 Chemistry

NCERT Solutions for Class 11 Physics

 

 

Recently Asked Questions

 

Related Articles

Exams
Articles
Questions