# 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

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.

## 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