The NCERT solutions for the questions given in Chapter 5, Complex Numbers and Quadratic Equations, of the Class 11 NCERT textbooks are available here. In this chapter, students learn about Complex Numbers and Quadratic Equations in detail. Students can easily score full marks in the questions asked from this chapter by solving all the questions present in the NCERT textbook.
The Class 11 NCERT solutions for Complex Numbers and Quadratic Equations are very easy to understand. These solutions cover all the exercise questions included in the book and are according to the latest guidelines of CBSE. Here, the PDF of the Class 11 Maths Chapter 5 NCERT solutions is available which can be downloaded and referred in online mode. Students can also avail these NCERT solutions and download it for free to practice them offline as well.
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NCERT Solutions for Class 11 Maths Chapter 5- Complex Numbers and Quadratic Equations
The major concepts of Maths covered in Chapter 5 – Complex Numbers and Quadratic Equations of NCERT Solutions for Class 11 includes:
5.2 Complex Numbers
5.3 Algebra of Complex Numbers
5.3.1 Addition of two complex numbers
5.3.2 Difference of two complex numbers
5.3.3 Multiplication of two complex numbers
5.3.4 Division of two complex number
5.3.5 Power of i
5.3.6 The square roots of a negative real number
5.4 The Modulus and the Conjugate of a Complex Number
5.5 Argand Plane and Polar Representation
5.5.1 Polar representation of a complex number
Exercise 5.1 Solutions 14 Questions
Exercise 5.2 Solutions 8 Questions
Exercise 5.3 Solutions 10 Questions
Miscellaneous Exercise On Chapter 5 Solutions 20 Questions
NCERT Solutions for Class 11 Maths Chapter 5 – Complex Numbers and Quadratic Equations
The chapter Complex Numbers and Quadratic Equations belongs to the unit Algebra, that adds up to 30 marks of the total 80 marks. There are 3 exercises along with a miscellaneous exercise in this chapter to help students understand the concepts related to Complex Numbers and Quadratic Equations clearly. Some of the topics discussed in Chapter 5 of NCERT Solutions for Class 11 Maths are as follows:
- A number of the form a + ib, where a and b are real numbers, is called a complex number, “a” is called the real part and “b” is called the imaginary part of the complex number
- Let z1 = a + ib and z2 = c + id. Then
- z1 + z2 = (a + c) + i (b + d)
- z1z2 = (ac – bd) + i (ad + bc)\
- For any non-zero complex number z = a + ib (a ≠ 0, b ≠ 0), there exists a complex number, denoted by or z–1, called the multiplicative inverse of z.
- For any integer k, i4k = 1, i4k + 1 = i, i4k + 2 = – 1, i4k + 3 = – i
- The polar form of the complex number z = x + iy is r (cosθ + i sinθ)
- A polynomial equation of n degree has n roots
Key Features of NCERT Solutions for Class 11 Maths Chapter 5- Complex Numbers and Quadratic Equations
Studying the Complex Numbers and Quadratic Equations of Class 11 enables the students to understand the following:
- Need for complex numbers, especially the square root of −1, to be motivated by the inability to solve every quadratic equation.
- Brief description of algebraic properties of complex numbers.
- Argand plane and polar representation of complex numbers.
- Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system, Square-root of a Complex number.