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

NCERT Solutions for Class 11 Maths Chapter 5: Are you feeling nervous about your performance in Class 11 Annual Exam? There is nothing wrong with that if we consider the challenges which fall under the Class 11 CBSE Course. A student needs to take care of different subjects while getting ready for the final exam. At this time a student needs proper guidelines which will help him or her to prepare in a better way.

Today we will be focusing on a chapter from the NCERT Maths book which is important for the competitive exams and the chapter is none other than 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

The solutions which have been presented in the NCERT solutions Chapter 5 will clear all your doubts or confusions regarding Complex Numbers and Quadratic Equations. The sections which we will be covering are connected with the overview of Chapter 5 along with the benefits of following NCERT solutions. You will also get to explore topic wise/ exercise wise explanations which have been highlighted in this blog. Read all the sections with a focused mind.

You can download CBSE NCERT Solutions for Class 11 Maths Chapter 5 from below.

## What will you learn in CBSE Class 11 Maths Chapter 5 – Complex Numbers and Quadratic Equations?

In Mathematics Class 11 Chapter 5 you will understand the different ways to solve problems in relation to the basic concepts of complex numbers, quadratic equation, algebraic properties of complex numbers, argand plane and polar representation of complex numbers, fundamental theorem of algebra, the square-root of a complex number. The Class 11 Mathematics NCERT Solutions Chapter 5 will prepare you for the final exam with the help of guidelines and examples.

The chapter Complex Numbers and Quadratic Equations might seem like a cup of tea when you go through the solutions on a regular basis. The chapter has dealt with the extension of the real number system and the moment you check all the solved answers you will be ready to face any questions from Complex Numbers and Quadratic Equations. The NCERT solutions can play the role of a guide because it has all the answers you need to apply the concepts which is based on complex numbers and quadratic equations. The experts have followed the latest CBSE pattern while shaping the NCERT Chapter 5 Solutions Maths and it is believed to be the perfect guidebook for your exam.

We will now highlight the subtopics which fall under the fifth chapter of NCERT solutions.

Class 11 Maths NCERT Solutions Chapter 5 Topic-Wise Listing

You will come across the questions from the following sub topics in the NCERT solutions-

Here are the topics/ subtopics of the chapter:

• 5.2 – Complex Numbers
• 5.3 – Algebra of Complex Numbers
• 5.3.1- Addition of two complex numbers
• 5.3.2 – Difference of two complex numbers
• 5.3.3 – Multiplication of two complex numbers
• 5.3.4 – Division of two complex number
• 5.3.5 – Power of i
• 5.3.6 – The square roots of a negative real number
• 5.3.7 – Identities
• 5.4 – The Modulus and the Conjugate of a Complex Number In this, you will find the modulus of a complex number, a conjugate
• 5.5 – Argand Plane and Polar Representation
• 5.5.1- Polar representation of a complex number

#### NCERT Solutions For Class 11 Maths Chapter 5 Exercise-wise listing

There are a total of 3 exercises along with miscellaneous exercise. Here is the number of

questions which you can expect from each exercise. You will also get all possible solutions and for this reason you need to relax.

• Exercise 5.1- 14 Questions along with Solutions
• Exercise 5.2 -8 Questions along with Solutions
• Exercise 5.3 -10 Questions along with Solutions
• The miscellaneous exercise consists of various questions with solutions

NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.1

In this exercise the students will be able to practice problems which are based on the extended system of Real Numbers. This section deals with the questions with the important mathematical concepts in relation to Complex Numbers and Quadratic Equations. Apart from this the other essential parts which have been dealt in the Class 11 Maths Chapter 5 NCERT Solutions are-

• Addition and difference of two complex numbers
• Difference between two complex numbers
• Multiplication of two complex numbers
• Division of two complex numbers
• Power of i
• The square roots of a negative real number
• The modulus and the conjugate of a complex number

Each problem has been addressed in the NCERT textbook with proper examples and it has also been solved in an effective way. When you get a copy of this you will undertand the relevance of purchasing Chapter 5 Maths NCERT Solutions.

### NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.2

In this exercise you will get all the guidelines from the NCERT Chapter 5 Maths Solutions which will boost your confidence. The problems which deal with basics of Complex Numbers and Quadratic Equations have been solved with proper explanations. After you attempt all the difficult questions you can sit with the NCERT Solutions Class 11 Maths Chapter 5. When you focus on the ways the problems are solved you will be amazed. The experts have tried to focus on the tiny details and when you take care of these little things your performance reaches a new height.

### NCERT Solutions for Class 11 Maths Chapter 5  Exercise 5.3

The 3rd exercise concentartes on different concepts which are connected with the Algebra of Complex Numbers. The students will get to know about some of the essential concepts like Addition of Two Complex Numbers, Difference of Two Complex Numbers, Multiplication of Two Complex Numbers, Division of Two Complex Numbers, Power of i, The Square Roots of a Negative Real Number, and Identities. You will come across different kinds of answers when you buy the NCERT solutions for yourself and you will also notice that the problems have been addressed in way which will be easier to digest. You don’t have to worry about the right answers all day when you are ready with the solutions.

### NCERT Solutions For Class 11 Maths Chapter 5 Miscellaneous

In the Miscellaneous Exercise Chapter 5 class 11 you will get all kinds of solutions which will help you to score good marks. The experts tried to cover all kinds questions which are associated with the basics of Complex Numbers and Quadratic Equations while designing the Chapter 5 Class 11 Maths Solutions . After you finish the important aspects of this chapter you need to solve the problems first. When you get stuck refer to the problems and that is probably the best way to learn.

## Theorems and formulas used in CBSE Class 11 Maths Chapter 5 – Complex Numbers and Quadratic Equations

A complex number is a number that can be expressed in the form p + iq, where p and q are real numbers, and i is a solution of the equation x2=−1. −1−−−√=i or i2=−1.

Examples of complex numbers: 8 – 2i, 2 +31i, 2+45i, etc. Complex numbers are denoted by ‘z’.

General form of Complex Number: z = p + iq

Where,

• p is known as the real part, denoted by Re z
• q is known as the imaginary part, denoted by Im z

If z = 12 + 35i, then Re z = 12 and Im z = 35. If z1 and z2 are two complex numbers such that z1 = p + iq and z2 = r + is. z1 and z2 are equal if p = r and q = s.

Algebra of Complex Numbers

Let z1 = m + ni and z2 = o + ip be two complex numbers. Then, z1 + z2 = z = (m + o) + (n + p)i, where z = resultant complex number. For example, (12 + 13i) + (-16 +15i) = (12 – 16) + (13 + 15)i = -4 + 28i.

1. The sum of complex numbers is always a complex number (closure law)
2. For complex numbers z1 and z2: z2 + z1= z1 + z2 (commutative law) For complex numbers z1, z2, z3: (z1 + z2) + z3 = z1 + (z2 + z3) [associative law].
3. For every complex number z, z + 0 = z [additive identity]
4. To every complex number z = p + qi, we have the complex number -z = -p + i(-q), called the negative or additive inverse of z. [z + (–z) = 0]

#### Difference of complex numbers

Let z1 = m + ni and z2 = o + ip be two complex numbers, then z1 – z2 = z1 + (-z2). For example, (16 + 13i) – (12 – 1i) = (16 + 13i) + (-12 + 1i ) = 4 + 14i and (12 – 1i) – (16 + 13i) = (12 – 1i) + ( -16 – 13i) = -4 – 14i

#### Multiplication of complex numbers

Let z1 = m + ni and z2 = o + ip be two complex numbers then, z1 × z2 = (mo – np) + i(no + pm). For example, (2 + 4i) (1 + 5i) = (2 × 1 – 4 × 5) + i(2 × 5 + 4 × 1) = -22 + 14i The product of two complex numbers is a complex number (closure law)

• For complex numbers z1 and z2, z1 × z2 = z2 × z1 (commutative law).
• For complex numbers z1, z2, z3, (z1 × z2) × z3 = z1 × (z2 × z3) [associative law].

Let z1 = m + in and z2 = o + ip. Then,

• z1 + z2 = (m + o) + i (n + p)
• z1 z2 = (mo – np) + i(mp + on)
• The conjugate of the complex number z = m + in, denoted by z¯¯¯, is given by z = m – in.

## Advantages of following NCERT Solutions for Class 11 Maths Chapter 5

When you focus on the NCERT solutions you will know about the benefits of following solutions based on Chapter 2 Maths Class 11. You will get enough reasons to buy NCERT solutions when you observe the contents of the solutions. Here are some of the benefits. After completing the syllabus you check it.

• NCERT solutions for Chapter 5 CBSE Class 11 Maths can help you to bring change in your methods of preparation.
• After analyzing the contents of the NCERT solutions you will be in a position to design your study materials. You will get new ideas to shape your study materials.
• Going through the important questions NCERT Chapter 5 Solutions is a must if you really want some clarity in relation to the topics. All the topics will be easier for you to understand if you explore the contents of Solutions NCERT carefully.
• You will be able to come up with an effective strategy after you examine the various concepts in connection with the solutions of Complex Numbers and Quadratic Equations on a regular basis.
• You will be able to appear for your Maths exam with a better plan if you keep the important points from the solutions in your mind.
• You will be able to complete your any kind of problems in relation to Complex Numbers and Quadratic Equations with full confidence when you follow the solutions.

We have covered the complete guide on CBSE NCERT Solutions for Class 11 Maths Chapter 5 – Complex Numbers and Quadratic Equations. Feel free to ask us any questions in the comment section below.