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NCERT Class 11 Mathematics Chapter 04 Complex Numbers and Quadratic Equations Digital Edition
For Class 11 Mathematics, this chapter in NCERT Book Class 11 Maths Complex Numbers And Quadratic Equations Questions provides a detailed overview of important concepts. We highly recommend using this text alongside the NCERT Solutions for Class 11 Mathematics to learn the exercise questions provided at the end of the chapter.
Chapter 04 Complex Numbers and Quadratic Equations NCERT Book Class Class 11 PDF (2025-26)
5.1 Overview
We know that the square of a real number is always non-negative e.g. (4)2 = 16 and (– 4)2 = 16. Therefore, square root of 16 is ± 4. What about the square root of a negative number? It is clear that a negative number can not have a real square root. So we need to extend the system of real numbers to a system in which we can find out the square roots of negative numbers. Euler (1707 - 1783) was the first mathematician to introduce the symbol i (iota) for positive square root of – 1 i.e., i = √−1 .
5.1.1 Imaginary numbers
Square root of a negative number is called an imaginary number., for example,
√−9 = √−1√ 9 = i3, √−7 = √−1 7 =i √7
5.1.2 Integral powers of i
i = √−1 , i 2 = – 1, i 3 = i 2 i = – i , i 4 = (i 2)2 = (–1)2 = 1.
To compute in for n > 4, we divide n by 4 and write it in the form n = 4m + r, where m is quotient and r is remainder (0 ≤ r ≤ 4)
Hence in = i4m+r = (i4)m . (i)r = (1)m (i)r = ir
For example, (i)39 = i 4 × 9 + 3 = (i4)9 . (i)3 = i3 = – i
and (i)–435 = i – (4 × 108 + 3) = (i)– (4 × 108) . (i)– 3
Please refer to attached file for NCERT Class 11 Maths Complex Numbers And Quadratic Equations Questions
| NCERT Book Class 11 Maths Relations And Functions |
| NCERT Book Class 11 Maths Relations And Functions Questions |
| CBSE Book Class 11 Maths Trigonometric Functions |
| NCERT Book Class 11 Maths Trigonometric Functions |
| NCERT Book Class 11 Maths Trigonometric Functions Questions |
| CBSE Book Class 11 Maths Complex Numbers |
| NCERT Book Class 11 Maths Complex Numbers And Quadratic Equations |
| NCERT Book Class 11 Maths Complex Numbers And Quadratic Equations Questions |
| NCERT Book Class 11 Maths Linear Inequalities |
| NCERT Book Class 11 Maths Linear Inequalities Questions |
| NCERT Book Class 11 Maths Permutations And Combinations |
| NCERT Book Class 11 Maths Permutations And Combinations Questions |
| NCERT Book Class 11 Maths Binomial Theorem |
| NCERT Book Class 11 Maths Binomial Theorem Questions |
| CBSE Book Class 11 Maths Sequence and Series |
| NCERT Book Class 11 Maths Sequences And Series |
| NCERT Book Class 11 Maths Sequences And Series Questions |
| CBSE Book Class 11 Maths Straight Line |
| NCERT Book Class 11 Maths Straight Lines |
| NCERT Book Class 11 Maths Straight Lines Questions |
| NCERT Book Class 11 Maths Conic Sections |
| NCERT Book Class 11 Maths Conic Sections Questions |
| NCERT Book Class 11 Maths Introduction To Three Dimensional Geometry |
| NCERT Book Class 11 Maths Introduction To Three Dimensional Geometry Questions |
| CBSE Book Class 11 Maths Limit and Derivatives |
| NCERT Book Class 11 Maths Limits And Derivatives |
| NCERT Book Class 11 Maths Limits And Derivatives Questions |
| NCERT Book Class 11 Maths Statistics |
| NCERT Book Class 11 Maths Statistics Questions |
| NCERT Book Class 11 Maths Probability |
| NCERT Book Class 11 Maths Probability Questions |
| NCERT Book Class 11 Maths Answers and Solutions |
| NCERT Book Class 11 Maths Answers and Solutions2 |
| NCERT Book Class 11 Maths Infinite Series |
| NCERT Book Class 11 Maths Mathematical Modelling |
Important Practice Resources for Class 11 Mathematics
NCERT Book Class 11 Mathematics Chapter 04 Complex Numbers and Quadratic Equations
Download the official NCERT Textbook for Class 11 Mathematics Chapter 04 Complex Numbers and Quadratic Equations, updated for the latest academic session. These e-books are the main textbook used by major education boards across India. All teachers and subject experts recommend the Chapter 04 Complex Numbers and Quadratic Equations NCERT e-textbook because exam papers for Class 11 are strictly based on the syllabus specified in these books. You can download the complete chapter in PDF format from here.
Download Mathematics Class 11 NCERT eBooks in English
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Benefits of using NCERT Class 11 Textbooks
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