# Higher Algebra Hall & Knight Surds & Imaginary Quantities (Chapter 8) Solutions

Hall and Knight Higher Algebra Solutions for Chapter 8 ‘Surds and Imaginary Quantities’ are prepared as per the latest syllabus for IIT JEE and Class 12 Maths. These solutions have been formulated to include all the important concepts of the chapter like rationalizing factor of roots and cubes, imaginary quantities and modulus of products. The chapter deals with the basics like moduli, powers of ώ cube roots of unity and powers of ‘i’. You will also learn about the concepts of conjugate, rationalization, elementary algebra and binomial theorem from the chapter.

Higher Algebra By H.S. Hall and S.R. Knight Surds and Imaginary Quantities Solutions have two exercises 75 questions. Once you solve these questions you will learn to deal with problems related to rational products, rationalizing factor, conjugates, binomials, cubes and inspection of cubes and roots. These exercises contain all possible kinds of questions which can be framed from these concepts for tough competitive exams like JEE Main and JEE Advanced.

Instasolv provides Elementary Algebra and Higher Algebra by Hall & Knight Solutions chapter-wise so that all your queries can be resolved at a single platform. All our solutions for Surds and Imaginary Quantities are based on the latest syllabus for higher algebra for JEE. Each question has been solved in a stepwise manner so that you can grasp the short cut tricks easily for quick calculations.

## Important Topics for Higher Algebra by Hall and Knight Chapter 8: Surds and Imaginary Quantities

**Rationalizing **

In this chapter, you will learn about the properties of rationalizing the denominators and numerators of the given fractions in order to express them in a particular manner and at some instances to solve them. In some cases, you will also have to rationalize the expressions by equating them with other terms. The property of rationalizing has been used very frequently in the chapter in numerous different questions.

**Modulus **

In case of the square root of a2+ b2 the positive value is termed as the modulus of each of the conjugate expression. Another important thing which you will have to keep in mind is that the modulus of the product of two imaginary expressions will be equal to the product of their moduli.

**Conjugate Expression **

In this chapter, you will learn about the various properties of imaginary expressions. One such property is the multiplication of the numerator and the denominator by the conjugate expression of the original one. In case if the denominator of a given fraction is expressed in the form of a + b -1 then you need to multiply and divide the numerator and the denominator of that fraction by it by a – b -1 (which is the conjugate expression of the term). You will also get to learn that the sum, difference, product and quotient of any imaginary expression in each and every scenario will result in an imaginary expression of the same form.

### Exercise Discussions of Hall and Knight Higher Algebra Solutions Chapter 8: Surds and Imaginary Quantities

**Example VIII a**

**The first exercise has a total of 44 questions.**It begins with a very simple question where you have to express the given fractions as equivalent fractions along with rational denominators.

- Then there are questions where you are required to solve the given values in order to find a factor which would rationalize it

- Question 13 – 18 include questions where you are required to express the given fractions with rational denominator

- There are some expressions which you are required to solve in order to find their square root and cube root

- There are some application-based questions along with some problems which are provided with conditions in order to derive answers.

**Example VIII b **

- This exercise includes questions which are based on imaginary quantities, coefficients and properties of imaginary quantities, and has a total of 31 questions.
- It begins with a simple problem where you are required to multiply the given expressions with one another
- Then there are some questions where you are required to express the given fraction with rational denominators
- There are some questions where you are required to find the square root and values of the given expression with the condition that they are positive integers.
- There are questions where you have to implement your understanding of the expression of terms and present the given expressions in the form of A + i B
- There are questions revolving around the cube roots of unity and somewhere you are required to prove the given terms by equating them with one another.
- Why Use Hall and Knight Higher Algebra Solutions Chapter 8: Surds and Imaginary Quantities by Instasolv
- Hall & Knight Algebra Mathematics book with solutions prepared by our subject matter experts deal with the questions in a step by step detailed manner and an easy language.
- We have given the particular emphasis on ensuring that all our answers are provided according to the up to date syllabus and curriculum.
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