# 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 include answers to all the exercises of the chapter. Refer to these solutions whenever you get stuck in understanding the chapter and solve all your doubts immediately. NCERT Solutions for Class 11 Maths Chapter 5 includes various topics such as algebra of complex numbers, identities of complex numbers, modulus and conjugate of a complex number, argand and polar representation of a natural number etc.

Chapter 5 has 4 exercises and 53 questions in total. Our step by step solutions will help you understand the concepts of the chapter and you will get enough time to practice more questions related to it. The chapter includes many important theorems that can only be learned by practising the solutions. We have also given a short summary of the chapter below to help you revise all the basic concepts. Our NCERT solutions will help you correct your mistakes as well as prove supportive in clearing your doubts in chapter 5.

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

NCERT Solutions for Class 11 Chapter 5 of Maths is subdivided into 7 sections. It also has 3 exercises and several examples besides a miscellaneous exercise to help you practice the problems. The syllabus is set out logically to enable you to grasp the difficult concepts in a sequential manner. They include:

- Introduction to Complex Numbers
- Algebra of Complex Numbers
- The Modulus and the Conjugate of a Complex Number
- Argand Plane and Polar Representation
- Quadratic Equations

In earlier classes, you have learned that not all quadratic equations have real solutions. Some of them also have imaginary solutions that are represented as complex numbers. Section 5.1 explains complex numbers in details with examples. Section 5.2 further explains about the real and imaginary parts of the complex numbers with suitable examples and illustrations.

The next section of the chapter, section 5.3, deals with addition, subtraction, multiplication, division of the two complex numbers apart from the square root of negative real numbers and the identities of complex numbers. You will get a clear understanding of one of the basic concepts of Algebra – BODMAS – Bracket, Of, Division, Multiplication, Addition, and Subtraction after studying this chapter.

Section 5.4 introduces you to the concept of Modulus and Conjugate of a Complex Number. For your easy understanding, this section includes several examples followed by detailed explanations.

Section 5.5 teaches you about the different pairs of complex numbers and the definition of Argand Plane or Complex Plane. It also teaches you the method to follow for the Polar Representation of Complex Numbers. The last section of the chapter deals with the Quadratic Equations, their types, and Polynomial Equations in detail.

### Exercise-wise Discussion for NCERT Solutions of Class 11 Maths Chapter 5

- There are 3 exercises at the end of chapter 5. The first exercise contains 14 questions dealing with concepts of expressing complex numbers, rationalizing, powers of complex numbers to perform additions, addition and subtraction of various types of complex numbers with varying powers.
- The second exercise has 8 questions focusing on finding modulus, arguments of complex numbers, expressing complex numbers in polar form and addition and subtraction of various forms of numbers.
- The third exercise has 10 questions focusing on solving quadratic equations.

### Benefits of NCERT Solutions for Class 11 Maths Chapter 5 by Instasolv

NCERT Class 11 Maths Chapter 5 is important from the perspective of CBSE exams. Our NCERT Solutions for Class 11 Maths Chapter 5 is a great tool to help you achieve maximum marks in the subject. Our solutions will help you solve all the problems of Chapter 5 with reason and logic – the two imperative tools in solving questions related to complex numbers.