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NCERT Book Class 11 Mathematics - Chapter 04 Complex Numbers and Quadratic Equations PDF
This chapter in NCERT Book Class 11 Maths Complex Numbers And Quadratic Equations makes learning easy for Class 11 Mathematics students. Read it carefully. Also, use the NCERT Solutions for Class 11 Mathematics to check answers for all the textbook questions.
Chapter 04 Complex Numbers and Quadratic Equations NCERT Book Class 11 PDF (2026-27)
5.1 Introduction
In earlier classes, we have studied linear equations in one and two variables and quadratic equations in one variable. We have seen that the equation x2 + 1 = 0 has no real solution as x2 + 1 = 0 gives x2 = – 1 and square of every real number is non-negative. So, we need to extend the real number system to a larger system so that we can find the solution of the equation x2 = – 1. In fact, the main objective is to solve the equation ax2 + bx + c = 0, where D = b2 – 4ac < 0, which is not possible in the system of real numbers.
5.2 Complex Numbers
Let us denote −1 by the symbol i. Then, we have 2 i = −1 . This means that i is a solution of the equation x2 + 1 = 0. A number of the form a + ib, where a and b are real numbers, is defined to be a complex number. For example, 
, are complex numbers.
For the complex number z = a + ib, a is called the real part, denoted by Re z and b is called the imaginary part denoted by Im z of the complex number z. For example, if z = 2 + i5, then Re z = 2 and Im z = 5. Two complex numbers z1 = a + ib and z2 = c + id are equal if a = c and b = d.
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NCERT Book Class 11 Mathematics Chapter 04 Complex Numbers and Quadratic Equations
Access the authorized NCERT Textbook for Class 11 Mathematics Chapter 04 Complex Numbers and Quadratic Equations, revised for the current academic year. Recognized as the core reading material across schools nationwide, educators strongly recommend the Chapter 04 Complex Numbers and Quadratic Equations e-textbook since board evaluations for Class 11 derive entirely from its syllabus guidelines. Easily download the complete chapter file in a convenient PDF format right here.
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