# RS Aggarwal Class 11 Chapter 5 Solutions (Complex Numbers And Quadratic Equations)

RS Aggarwal Class 11 Solutions for Chapter 5 are a must if you are having difficulties in understanding this chapter. Quadratic Equation is an important concept not only for CBSE exams but also for entrance tests such as BITSAT, JEE, NEET, IPU-CET etc. Chapter 5 of RS Aggarwal book will give you a brief idea about topics like arithmetic operations on complex numbers, finding roots of quadratic equations and determining their nature.

The chapter consists of 7 exercises and with around 142 questions. These questions are related to important topics like the algebra of complex numbers, modulus, and the conjugate of complex numbers, solutions of quadratic equations, etc. RS Aggarwal Solutions book also gives a deep analysis of the topics using solved examples. You must practice all the questions of the chapter in order to score well in your exams and enhance your knowledge regarding the chapter

Instasolv team is going to help you in all ways to make the course content easy for you. We have the subject matter experts who will make all the questions easy for you as we provide you with a detailed explanation of every question. Given below is a short summary of the chapter to help you revise its basic concepts quickly.

## Important Points for RS Aggarwal Class 11 Solutions for Chapter 5

**Quadratic Equation: **A polynomial of the second degree is called a quadratic polynomial. Polynomials of degree three and four are known as cubic and biquadratic polynomials respectively. A quadratic polynomial f(x), when equated to zero, is called a quadratic equation.

**Roots of a Quadratic Equation: **The values of variable x. Which satisfies the quadratic equation is called the root of a quadratic equation. You will know different ways of finding a quadratic equation:

- Factorization Method
- Direct Formula
- Nature of Roots
- Conjugates Roots
- Roots Under Particular Conditions

### Important Points To Be Remembered

- The general form of a complex number: z = p+iq, p is known as the real part, denoted by Re z, q is known as the imaginary part, denoted by Im z
- Two complex numbers are said to be conjugate of each other if their sum is real and their product is also real.
- Any complex number a+ib can be written in an ordered pair as (a,b), where a is the real part and b is the imaginary part of a complex number.
- Any equation containing a variable of highest degree 2 is known as a quadratic equation.
- The values of variables satisfying a given equation are known as its roots.
- An equation of degree n has n roots, real or imaginary.
- An odd degree equation has at least one real root whose sign is opposite to that of its last term (constant term), provided that the coefficient of highest degree term is positive.
- Every equation of an even degree whose constant term is negative and the coefficient of the highest degree is positive has at least two real roots, one positive and one negative.
- If an equation has only one change of sign it has one positive root.
- If all terms of an equation are positive and the equation involves odd power of x, then all its roots are complex.

### Exercise-Wise Discussion of RS Aggarwal Solutions for Class 11 Chapter 5

- There are 7 exercises in the chapter with a total of 142 questions. This means you will have ample questions to practice and revise the concepts of the chapter.
- Exercise 1 has 15 questions in which you have to evaluate the value of ‘i’.
- Exercise 2 has 28 questions in which you have to simplify complex numbers, find their inverse, conjugate and modulus.
- Exercise 3 has 12 questions based on arithmetic of complex numbers.
- Exercise 4 has 24 questions in which you need to find the modulus and argument of the given complex numbers and express them in polar form.
- Exercise 5 has 21 questions where you need to solve the given quadratic equations.
- Exercise 6 contains 14 questions in which you need to evaluate the complex numbers.
- Exercise 7 contains 28 questions of very short answer type. You are asked to evaluate the complex numbers, express numbers in the form of ai+b, write the numbers in polar form etc. in this exercise.

### Benefits of RS Aggarwal Solutions for Class 11 Chapter 5 by Instasolv

If you have done all the NCERT questions related to Complex Numbers and Quadratic Equations and want to practice more advanced questions, then nothing is better than RS Aggarwal Class 11 Maths Solutions Book. This book is going to help you in building a strong base so that you can perform well in your final exams. It is a good reference book for JEE and NEET preparation as well. Try to solve the questions given in the book and if you face any sort of issues our RS Aggarwal Solutions for Class 11 Chapter 5 will help you out. Our solutions are 100% correct with step-wise explanations and clarity.