NCERT Solutions for Class 11 Mathematics Chapter 4 Complex Numbers and Quadratic Equations
NCERT solutions for Class 11 Mathematics Chapter Complex Numbers and Quadratic Equations – complete answers & explanations
Complex numbers and quadratic equations is an important chapter in Class 11 Mathematics that introduces students to a new number system beyond real numbers. In this chapter, students learn how to work with imaginary numbers, understand algebraic operations on complex numbers, and solve equations that do not have real solutions. This topic builds a strong foundation for higher mathematics and is very useful for exams. These NCERT solutions provide clear and reliable answers that help students understand the correct approach to solving each question. Download the worksheet and practice alongside solutions for better clarity. Book a free trial now to get expert guidance and strengthen your understanding with personalised support.
What this NCERT chapter covers?
1. Introduction to complex numbers and
why they are needed to solve equations like x² + 1 = 0
2. Understanding the form a + ib, where a is the real part and b is the imaginary part
3. Learning about the imaginary unit i and its properties
4. Algebra of complex numbers including addition, subtraction, multiplication, and division
5. Important properties such as closure, commutative, and associative laws
6. Concept of multiplicative inverse and identity in complex numbers
7. Powers of i and patterns involved in simplifying expressions
8. Square roots of negative real numbers using complex numbers
9. Modulus and conjugate of a complex number and their applications
10. Argand plane and graphical representation of complex numbers
11. Understanding identities and expressions involving complex numbers
12. Application-based problems and mixed practice for exam preparation
How to use these NCERT solutions?
1. Start by solving each question
from the worksheet on your own without looking at the answers
2. Compare your answers step-by-step with the given solutions to check accuracy
3. Focus on understanding the method used rather than just memorising answers
4. Revise incorrect questions and try solving them again independently
5. Use the solutions as a guide to improve your problem-solving approach
6. Follow the exact order of questions to stay aligned with the worksheet structure
7. Practice regularly to build confidence in handling complex numbers
8. Parents and teachers can guide students by discussing tricky questions and concepts
9. Use these solutions during revision to quickly recall important formulas and methods
Important tips & tricks for students
1. Always write complex numbers in the standard form a + ib
2. Be careful while performing operations involving i, especially powers of i
3. Double-check signs during addition and subtraction
4. Use proper formulas for multiplication and division of complex numbers
5. Remember key identities and properties to simplify calculations
6. Practice converting expressions into a + ib form accurately
7. Avoid skipping steps as it may lead to calculation errors
8. Understand the concept of conjugate and modulus clearly
9. For activity or proof-based questions, focus on the correct method and logic
10. Regular practice is key to mastering this chapter
NCERT solutions – complete answer key
EXERCISE 4.1
1
0 + (1/25)i
2
0 + (1/3)i
3
0 – (1/3)i
4
14i
5
2 – 7i
6
(3/5) + (7/10)i
7
(2/3) + (4/3)i
8
–4
9
(1/9) + (1/3)i
10
(1/3) – (1/3)i
11
(4/25) + (3/25)i
12
(5/34) – (3/34)i
13
i
14
(8/13) + (11/13)i
MISCELLANEOUS EXERCISE ON CHAPTER 4
1
–1
2
0
3
x = 3, y = –3
4
Verified
5
Verified
6
Verified
7
Verified
8
(i) 1
(ii) 1
9
1
10
1
11
1
12
0
13
Verified
14
4
Why NCERT solutions help students?
NCERT solutions help students prepare effectively for exams by providing the correct method of solving each question. They improve concept clarity, ensure answers follow the expected format, and build confidence in tackling different types of problems. With regular practice, students can develop strong problem-solving skills and perform better in Mathematics.
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