NCERT Exemplar Class 11 Maths Chapter 5 Solutions: Complex Numbers and Quadratic Equations
NCERT Exemplar Solutions for Class 11 Maths Chapter 5 is prepared by Instasolv to boost up your confidence during the exams. Complex Numbers and Quadratic Equations is an important chapter of NCERT Exemplar Class 11 Maths in class 12 maths, competitive exams, and also for your college-level studies. At Instasolv, you will find the solutions sufficient for clarifying your doubts and satisfying your queries.
Some of the important topics of Chapter 5 – Complex Numbers and Quadratic Equations include imaginary numbers, complex numbers, integral power of i, modulus of a complex number, conjugate of a complex number, properties of modulus of a complex number, power of imaginary number i, the square root of a negative real number, solutions for quadratic equations, addition, difference, multiplication and division of two complex numbers.
NCERT Exemplar Class 11 Maths Solutions Chapter 5 has 6 exercises with around 83 questions in total. All these solutions are developed by expert maths teachers who have broadened and simplified the concepts of complex numbers and quadratic equations for better understanding.
Important Topics for NCERT Maths Exemplar Solutions Class 11 Chapter 5 – Complex Numbers and Quadratic Equations
What are Complex Numbers?
The complex numbers are the numbers that can be stated in the form p + iq, where p and q are real numbers, and i is a solution of the equation x2 = -1. For example, 8 – 2i and 2 +31i. Complex numbers are represented by ‘z’.
The general form of a complex number can be represented as z = p + iq
where,
- p is called as the real part, represented by Re z
- q is called as the imaginary part, represented by Im z
If z = 6 + 25i, then Re z = 6 and Ix z = 25. Let’s suppose, z1 and z2 are two complex numbers where z1 = p + iq and z2 = r + is. z1 and z2 are equal to each other if p = r and q = s.
Algebra of Complex Numbers
- Addition of complex numbers
Let z1 = x + yi and z2 = o + ip be two complex numbers. Then, z1 + z2 = z = (x + o) + (y + p)i, where z = resultant complex number. For example, (12 + 13i) + (-16 +15i) = (12 – 16) + (13 + 15)i = -4 + 28i.
- Difference of complex numbers
Let z1 = x + yi and z2 = o + ip be two complex numbers, then z1 – z2 = z1 + (-z2). For example, (16 + 13i) – (12 – 1i) = (16 + 13i) + (-12 + 1i) = 4 + 14i and (12 – 1i) – (16 + 13i) = (12 – 1i) + (-16 – 13i) = -4 – 14i
- Multiplication of complex numbers
Let z1 = x + yi and z2 = o + ip be two complex numbers then, z1 × z2 = (xo – yp) + i(yo + px). For example, (2 + 4i) (1 + 5i) = (2 × 1 – 4 × 5) + i(2 × 5 + 4 × 1) = -22 + 14i.
Exercise-wise Discussion of NCERT Maths Exemplar Solutions Class 11 Chapter 5 – Complex Numbers and Quadratic Equations
Chapter 5 has 6 main exercises with a total of 83 questions. The detailed description of these exercises is provided below:
Exercise 5.1 – Solved Examples
The first exercise of Chapter 5 – Complex Numbers and Quadratic Equations consist of solved examples for your reference. It has 32 questions that contain short answer type questions, long answer type questions, and objective type questions based on all the important topics of the chapter.
Exercise 5.2 – Short Answer Type Questions
NCERT Exemplar Class 11 for Maths Chapter 5 Exercise 5.2 has a total of 11 questions. These questions are based on the topics of imaginary numbers, complex numbers, integral power of i, modulus of a complex number, and the conjugate of a complex number.
Exercise 5.3 – Long Answer Type Questions
This exercise consists of a total of 13 questions based on the properties of modulus of a complex number, power of imaginary number i, the square root of a negative real number, solutions for quadratic equations, addition, difference, multiplication and division of two complex numbers.
Exercise 4, 5, and 6 contain 26 questions in total. While practising these exercises you will find the very short answer type questions including fill in the blanks, multiple-choice questions, and state true or false.
Why Use NCERT Maths Exemplar Solutions Class 11 Chapter 5 – Complex Numbers and Quadratic Equations by Instasolv?
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- You will get a better understanding of solving these exercises and it will also help you to score high marks.
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