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

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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

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