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RD Sharma Class 11 Solutions Chapter 13 - Complex Numbers (Ex 13.3) Exercise 13.3

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Last updated date: 19th May 2024
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Solutions for the Class 11 Chapter 13 Complex Numbers of the RD Sharma Book are Available for a Free Download at Vedantu

Free PDF download of RD Sharma Class 11 Solutions Chapter 13 - Complex Numbers Exercise 13.3 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 13 - Complex Numbers Ex 13.3 Questions with Solutions for RD Sharma Class 11 Maths to help you to revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams.


Students may have some familiarity with complex numbers, but to understand the complex numbers thoroughly students are required to have a practice of the chapter. Hence, RD Sharma class 11 Mathematics book provides the students with that practice and the best part - Vedantu provides solutions to ensure you have the current material to supplement it.


Practising the questions from the RD Sharma class 11 Maths is necessary because it is equally important for the students to check their progress. Therefore, Vedantu provides the students with the complete solutions for the class 11 RD Sharma Chapter 13 Complex Numbers exercise 13.3.


Also, if you are looking for the solutions of the next chapter, that is, chapter number 14 Quadratic Equations, you can find it here: RD Sharma Class 11 Solutions Chapter 14 - Quadratic Equations.

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An Overview of the Solutions for the Class 1 RD Sharma, Exercise 13.3

  • In exercise 13.3 of the RD Sharma class 11 Mathematics, there are a total of 9 questions given on the complex number.

  • Solutions of all these 9 questions of exercise 13.3 are given in the PDF file format for the students to download.

  • The PDF file is free to download for all the students of class 11, for the Subject of Mathematics.


Solved Examples

1. Find the square root of – 5 + 12i

(i) Given is:

– 5 + 12i

We know that, Z = a + ib

So, (a + ib) = (-5+12i)

Here, b > 0

Let us now simplify,

 

\[\sqrt{-5+12i}= \pm \left [ \left ( \frac{-5+\sqrt{\left ( -5 \right )^{2}+12^{2}}}{2} \right )^{\frac{1}{2}} +i\left (   \frac{5+\sqrt{\left ( -5 \right )^{2}+12^{2}}}{2} \right )^{\frac{1}{2}}  \right ]\]

                                                                                                                                       [Since,b>0]


=\[\pm \left [ \left ( \frac{-5+\sqrt{\left ( 25 \right )+144}}{2} \right )^{\frac{1}{2}} +i\left (   \frac{5+\sqrt{\left ( 25 \right )+144}}{2} \right )^{\frac{1}{2}}  \right ]\]

= \[\pm \left [ \left ( \frac{-5+\sqrt{169}}{2} \right )^{\frac{1}{2}} +i\left (   \frac{5+\sqrt{ 169}}{2} \right )^{\frac{1}{2}}  \right ]\]

= \[\pm \left [ \left ( \frac{-5+13}{2} \right )^{\frac{1}{2}} +i\left (   \frac{5+13}{2} \right )^{\frac{1}{2}}  \right ]\]

= \[\pm \left [ \left ( \frac{8}{2} \right )^{\frac{1}{2}} +i\left (   \frac{18}{2} \right )^{\frac{1}{2}}  \right ]\]

= \[\pm \left [ 4^{\frac{1}{2}} +i9^{\frac{1}{2}}  \right ]\]

= \[\pm \left [ 2+3i \right ]\]

 

∴ Hence, Square root of (– 5 + 12i) is ±[2 + 3i]


Hence this article is useful for the students to understand the solutions of RD Sharma  Chapter 13 - Complex Numbers (Ex 13.3) Exercise 13.3.

FAQs on RD Sharma Class 11 Solutions Chapter 13 - Complex Numbers (Ex 13.3) Exercise 13.3

1. What are complex Numbers?

For understanding the complex numbers, lets us take a look at the real and Imaginary numbers:

  • Real numbers: It includes all the numbers of Mathematics, that is to say, rational and irrational, positive and Negatives. For example, 6, -1, 2.5 etc.

  • Imaginary numbers: These are the numbers whose square root is expressed in the negative number. Example √-1Complex Number: The combination or the sum of the Real and Imaginary numbers are the complex numbers.

You must check chapter number 13 of the class 11 RD Sharma Mathematics book, for a better understanding of the topic.

2. Are 0 and √-2 complex numbers?

As already discussed, all the numbers of Mathematics are included in the real number, and real numbers are part of the complex number. So, the number 0 is a real number, and therefore it is a complex number as well.  Now coming to the √-2, It is an imaginary number, because it is a root expressed in a negative number, and since along with the real numbers, imaginary numbers are also a part of complex numbers √-2 becomes a complex number as well.

3. I am having a problem solving a few of the questions of the class 11 RD Sharma Mathematics book exercise 13.2, what should I do?

If you are having a problem solving any questions of the class 11 RD Sharma Mathematics book, then it is totally fine. Because it happens, so first of all try to understand the question and give it a few more tries. Even after those tries, you are unable to solve the questions, then simply check the solution of exercise 13.3 of the class 11 RD Sharma Mathematics book, and try to understand the steps of solving the question. Lastly, solve the question by yourself once again.

4. Where can I find the solutions for the class 11 RD Sharma Mathematics book exercise 13.2?

You can find the solutions for the class 11 RD Sharma Mathematics book exercise 13.2 here on the website of Vedantu. Yes, Vedantu provides the complete solutions for each of the questions, that is to say, 9 questions. Also, these questions are solved by the top educators who have years of experience, not only in the field of Mathematics but also in teaching Mathematics to the students of class 11. Furthermore, these solutions are provided in PDF file format, which is completely free for download.