NCERT Class 11 Mathematics Mathematics: Chapter 4 — MATHEMATICS
This chapter introduces complex numbers as an extension of the real number system to solve quadratic equations with negative discriminants. It defines a complex number in the form a + ib, where 'a' is the real part and 'b' is the imaginary part. The chapter details the algebra of complex numbers, including addition and subtraction, and outlines the properties of addition such as closure, commutativity, associativity, and the existence of additive identity and inverse. It provides examples to illustrate these concepts, enabling students to solve equations that were previously unsolvable within the real number system and preparing them for advanced mathematical concepts in CBSE Class 11 Mathematics.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 11 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 4 — MATHEMATICS |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 4 minutes |
| Word count | 722 |
Learning outcomes
- Understand the need for complex numbers to solve quadratic equations.
- Define complex numbers in the form a + ib.
- Identify the real and imaginary parts of a complex number.
- Perform addition and subtraction of complex numbers.
- Understand the properties of addition for complex numbers.
Vocabulary
| Word | Meaning |
|---|---|
| Complex Number | A number of the form a + ib, where a and b are real numbers. |
| Real Part | The real number 'a' in a complex number a + ib, denoted as Re z. |
| Imaginary Part | The real number 'b' in a complex number a + ib, denoted as Im z. |
| Additive Identity | The complex number 0 + i0 (or 0) such that z + 0 = z. |
| Additive Inverse | For a complex number z = a + ib, its additive inverse is -z = -a + i(-b). |
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Practice questions
- Define a complex number. Answer: A complex number is a number of the form a + ib, where a and b are real numbers and i = sqrt(-1).
- What are the real and imaginary parts of the complex number 5 - 7i? Answer: The real part is 5 and the imaginary part is -7.
- Find the sum of (3 + 4i) and (2 - 5i). Answer: (3 + 2) + i(4 - 5) = 5 - i
- What is the additive inverse of -2 + 3i? Answer: The additive inverse is -(-2 + 3i) = 2 - 3i.
Practice MCQs
Q1. What is the imaginary unit 'i' defined as?
Explanation: The imaginary unit 'i' is defined as the square root of -1, which allows for the solution of equations like
Q2. For a complex number z = a + ib, what is 'a' called?
Explanation: 'a' is the real part of the complex number z = a + ib, denoted as Re z.
Q3. Which property states that z1 + z2 = z2 + z1 for complex numbers?
Explanation: The commutative law states that the order of addition does not affect the sum for complex numbers.
Q4. What is the additive identity for complex numbers?
Explanation: The additive identity is the complex number 0 + i0 (or simply 0), such that z + 0 = z.
Q5. If 4x + i(3x – y) = 3 + i(–6), what is the value of x?
Explanation: By equating the real parts, 4x = 3, which gives x = 3/4.
Frequently asked questions
Why do we need complex numbers in mathematics?
Complex numbers are needed to solve quadratic equations that have no real solutions, such as x^2 + 1 = 0, and to extend the number system for broader mathematical applications.
What is the imaginary unit 'i'?
The imaginary unit 'i' is defined as the square root of -1 (i = sqrt(-1)).
How are two complex numbers equal?
Two complex numbers z1 = a + ib and z2 = c + id are equal if their real parts are equal (a = c) and their imaginary parts are equal (b = d).
What is the sum of two complex numbers z1 = a + ib and z2 = c + id?
The sum is defined as z1 + z2 = (a + c) + i(b + d).
What is the additive inverse of a complex number z = a + ib?
The additive inverse of z is -z = -a + i(-b), such that z + (-z) = 0.
Does the addition of complex numbers satisfy the commutative law?
Yes, the addition of complex numbers satisfies the commutative law, meaning z1 + z2 = z2 + z1 for any two complex numbers z1 and z2.
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NCERT Class 11 Mathematics — Mathematics — Chapter 4 — MATHEMATICS. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.