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# Complex Numbers & Quadratic Equations NCERT Solutions Class 11 Maths Chapter 5 Exercise 5.1 5.2 5.3 Miscellaneous Free pdf Study Material Notes download-Anand Classes

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations of Maths help students in solving problems quickly, accurately and efficiently. Also, ANAND CLASSES’S provides complete solutions for all NCERT problems, thereby ensuring students understand them and clear their school board exams with good marks. These NCERT Solutions from ANAND CLASSES’S help students who aim to clear their school board exams even with last-minute preparations.

# Complex Numbers and Quadratic Equations Class 11 Maths Chapter 5 Miscellaneous Exercise

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

Chapter 5 of Class 11 Complex Numbers and Quadratic Equations has 3 exercises and a miscellaneous exercise to help the students practise the required number of problems to understand all the concepts. The topics and sub-topics discussed in the PDF of NCERT Solutions for Class 11 of this chapter include

### 5.1 Introduction

We know that some of the quadratic equations have no real solutions. That means the solution of such equations includes complex numbers. Here, we have found the solution of a quadratic equation such as ax2 + bx + c = 0 where discriminent D = b2 – 4ac < 0.

### 5.2 Complex Numbers

Definition of complex numbers, examples and explanations about the real and imaginary parts of complex numbers have been discussed in this section. Class 11 Maths NCERT Supplementary Exercise Solutions PDF helps the students to understand the questions in detail.

### 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

After studying these exercises, students are able to understand the basic BODMAS operations on complex numbers, along with their properties, power of i, square root of a negative real number and identities of complex numbers.

### 5.4 The Modulus and the Conjugate of a Complex Number

The detailed explanation provides the modulus and conjugate of a complex number with solved examples.

### 5.5 Argand Plane and Polar Representation

5.5.1 Polar representation of a complex number

In this section, it has been explained how to write the ordered pairs for the given complex numbers, the definition of a Complex plane or Argand plane and the polar representation of the ordered pairs in terms of complex numbers.

1. A number of the form a + ib, where a and b are real numbers, is called a complex number, “a” is called the real part, and “b” is called the imaginary part of the complex number
2. Let z1 = a + ib and z2 = c + id. Then
1. z1 + z2 = (a + c) + i (b + d)
2. z1z2 = (ac – bd) + i (ad + bc)
3. For any non-zero complex number z = a + ib (a ≠ 0, b ≠ 0), there exists a complex number, denoted by 1/z or z–1, called the multiplicative inverse of z
4. For any integer k, i4k = 1, i4k + 1 = i, i4k + 2 = – 1, i4k + 3 = – i
5. The polar form of the complex number z = x + iy is r (cosθ + i sinθ)
6. A polynomial equation of n degree has n roots.

## Frequently Asked Questions on NCERT Solutions for Class 11 Maths Chapter 5

Q1

### What are the topics covered under each exercise of NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations?

The NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations has exercise-wise problems, which cover equations related to quadratic equations and complex numbers. These solutions provide the students with clarity on concepts and theorems of complex numbers. This chapter has three exercises for which the solutions are provided here in PDF format. The first exercise deals with determining the multiplicative inverse, the second exercise deals with the modulus and argument of a given set of numbers, and the third exercise deals with solving quadratic equations.

Q2

### Explain the marks distribution in NCERT Solutions for Class 11 Maths.

There are about 6 units in the NCERT Solutions for Class 11 Maths in which the marks are distributed.
First unit – Sets and Functions (60 marks)
Second unit – Algebra (30 marks)
Third unit – Coordinate Geometry (10 marks)
Fourth unit – Calculus (30 marks)
Fifth unit – Mathematical Reasoning, Statistics (10 marks)
Sixth unit – Probability (30 marks)

Q3

### Does ANAND CLASSES’S give the most reliable answers in Chapter 5 of NCERT Solutions for Class 11 Maths?

The most accurate and reliable NCERT Solutions for Class 11 Maths Chapter 5 are available on ANAND CLASSES’S APP. Students can easily download the solutions, which are present in PDF format and access them during their exam preparation. The solutions are framed and compiled by a set of expert faculty who possess numerous years of experience in the respective subjects. The most detailed solutions to the exercise-wise problems are curated with the aim of helping students ace the exam without fear.

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