# NCERT Solutions for Class 11 Maths Chapter 5

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Exercise 5.1, Exercise 5.2, Exercise 5.3 and Miscellaneous Exercises for CBSE First Term Exam in English and Hindi Medium for session 2021-22.

UP Board Class 11 Maths Solution Chapter 5 in Hindi Medium. Class 11 Maths chapter 5 Test of Complex Numbers and Quadratic Equations 5.1 or Exercise 5.2 or Exercise 5.3 or Miscellaneous Exercise 5 in Hindi Medium is also available to or view online or download in PDF. Join the Discussion Forum to share your views. UP Board students can download UP Board Solutions for class 11 Chapter 5 here in PDF file format.

## NCERT Solutions for Class 11 Maths Chapter 5

• ### 11th Maths Chapter 5 Solutions in PDF

 Class: 11 Maths (English and Hindi Medium) Chapter 5: Complex Numbers and Quadratic Equations

### 11th Maths Chapter 5 Solutions

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers Exercise 5.1 to 5.3 and miscellaneous exercise are given below in updated format for current academic session 2021-22. All Solutions are updated for CBSE Exam 2021 based on new CBSE Curriculum 2021-2021 for CBSE Board, MP Board, Gujrat UP Board, Uttarakhand Board and Bihar Board, who are following NCERT Books 2021-22 for their exams.

#### Class 11 Maths Chapter 5 Exercise 5.1 Solution in Videos

Class 11 Maths Chapter 5 Exercise 5.1 Solution
Class 11 Maths Exercise 5.1 Solution in Hindi

#### Class 11 Maths Chapter 5 Exercise 5.2 Solution in Videos

Class 11 Maths Chapter 5 Exercise 5.2 Solution
Class 11 Maths Exercise 5.2 Solution in Hindi

#### Class 11 Maths Chapter 5 Exercise 5.3 Solution in Videos

Class 11 Maths Chapter 5 Exercise 5.3 Solution
Class 11 Maths Exercise 5.3 Solution in Hindi

#### Class 11 Maths Chapter 5 Miscellaneous Exercise Solution in Videos

Class 11 Maths Chapter 5 Miscellaneous Exercise Solution
Class 11 Maths Chapter 5 Miscellaneous Solution in Hindi

What is meant by Argand plane?
The coordinate plane that represents the complex numbers is called the complex plane or the Argand plane.

#### Important Terms on Complex Numbers

1. A number of the form z = a + ib, where a, b are real numbers, is called a complex number. a is called the real part of z, denoted by Re(z) and b is called the imaginary part of z, denoted by Im(z).
2. a + ib = c + id if a = c, and b = d

3. If z1 = a + ib, z2 = c + id. In general, we cannot compare and say that z1> z2 or z1< z2 but if b, d = 0 and a > c then z1> z2, i.e. we can compare two complex numbers only if they are purely real.
i). z = 0 + i 0 is additive identity of a complex number.
ii). –z = –a –ib is called the Additive Inverse or negative of z = a + ib.
iii). z = 1 + i 0 is multiplicative identity of complex number.

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### Important Questions on 11th Maths Chapter 5

##### Express the following complex number in the form a + ib: i⁹ + i¹⁹

i⁹ + i¹⁹
= (i⁴)².i + (i⁴)⁴.i².i
= (1)².i + (1)⁴.(-1).i [∵ i⁴ = 1 and i² = – 1]
= i – i = 0 = 0 + i0

##### Solve the following equation: 2x² + x + 1 = 0.

The given quadratic equation is 2x² + x + 1 = 0.
On comparing the given equation with ax² + bx + c = 0, we obtain a = 2, b = 1, and c = 1
So, the discriminant of the given equation is given by
D = b² – 4ac = 1² – 4×2×1 = -7
Therefore, the required solutions are
x = (-b±√D)/2a = (-1 ± √(-7))/(2×2) = (-1±√7. √(-1))/4 = (-1±√7 i)/4
[∵ √(-1)=i]

##### Which main topics will students study in chapter 5 of class 11th Maths?

The main topics that students will study in chapter 5 of class 11th Maths are:

1. What are complex numbers?
2. Algebra of complex numbers (Addition two complex numbers, Difference two complex numbers, Multiplication two complex numbers, Division of two complex numbers).
3. Power of i.
4. The square root of a negative real number.
5. The modulus and the conjugate of a complex number.
6. Argand plane and polar representation.
##### How many problems are there in chapter 4 of class 11th Maths?

Chapter 4 of grade 11th Maths has 4 exercises. The first exercise (Ex 5.1) has 6 examples (examples 1, 2, 3, 4, 5, 6) and 14 questions. In the second exercise (Ex 5.2), there are two examples (examples 7, 8) and 8 questions. The third Exercise (Ex 5.3) contains three examples (examples 9, 10, 11) and ten questions. The last (miscellaneous) exercise has five examples (examples 12, 13, 14, 15, 16) and 20 questions. So, there are 68 problems (16 examples and 52 questions) in chapter 4 of class 11th Maths.

##### Which problems of chapter 5 of class 11th Maths are expected for exams?

Problems of chapter 5 of class 11th Maths that are most important for the exams are:
1. Questions 10 and 14 of exercise 5.1.
2. Questions 5, 6, 7, and 8 of exercise 5.2.
3. Question 1, 7, 8, 9, and 10 of exercise 5.3.
4. Questions 4, 5, 10, 11, 14, 16, 17, 18, 19, and 20 of miscellaneous exercise on chapter 5.
5. Examples 9, 11, 16, 14, 15, and 16.

##### Is chapter 5 of class 11th Maths complicated?

Chapter 5 of class 11th mathematics is not easy and not complicated. It lies in the middle of easy and hard because some problems of this chapter are easy, and some are difficult. But difficulty level of any chapter varies from student to student. So, Chapter 5 of class 11th mathematics is easy or not depends on students also. Some students find it hard, some find it simple, and some find it in the middle of simple and hard.                                    