NCERT Solutions For Class 11 Maths Chapter 5: The chapter Complex Numbers and Quadratic Equations requires a lot of focus as it has lots of formulas. Often students are unable to remember those formulas or apply them properly and end up scoring low marks. To help students with their preparation, expert faculty at Embibe has prepared these NCERT solutions for 11th Class Mathematics Chapter 5. These NCERT Solutions for Class 11 Maths are based on the latest NCERT books for Class 11.
In this article, we will provide the PDF of the CBSE Class 11 Maths Chapter 5 solutions. Students can download the solutions for free without having to sign up.
CBSE NCERT Solutions For Class 11 Maths Chapter 5: Complex Numbers And Quadratic Equations
CBSE Class 11 Maths Chapter 5 covers the following topics:
|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 Numbers|
|5.3.5||Power of i|
|5.3.6||The Square mysqladmins 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|
NCERT Solutions For Class 11 Maths Chapter 5 PDF Download
Check out the NCERT Solutions for Class 11 Maths Chapter 5 here. You can also download the CBSE Class 11 Maths Chapter 5 Solutions PDF for free.
CBSE Class 11 Maths Chapter 5: Complex Numbers And Quadratic Equations
Bhaskara, an Indian mathematician, writes in his work Bijaganita, in 1150 A.D., “There is no square root of a negative quantity, for it is not a square.”
Cardan (1545 A.D) considered the problem of solving x+y=10, xy=40. He obtained x=5+√-15 and y=5-√-15 as the solution of it, which was discarded by him by saying that these numbers are ‘useless.’
Albert Girand (about 1625 A.D.) accepted the square root of negative numbers.
Euler was the first to introduce the symbol i for √-1 and W.R.Hamilton (about 1830 A.D.) regarded the complex number a+ib as an ordered pair of real numbers (a, b); thus, giving it a purely mathematical definition and avoiding the use of the so-called ‘Imaginary Numbers’.
In this chapter, you will learn about all these things about complex numbers.
How To Prepare For CBSE Class 11 Maths Chapter 5
Complex Numbers And Quadratic Equations requires a student to focus on his problem-solving skills. The questions in the chapter are concept-based which are taught before each exercise. So, go through the chapter from the NCERT book and understand the concepts first. Then go through the examples. After that, try to solve the exercise questions on your own. If you get stuck in between, refer to the solutions provided here.
Frequently Asked Questions On Class 11 Maths NCERT Chapter 5 PDF Download
Here are some of the frequently asked questions on NCERT Solutions for Class 11 Maths Chapter 5 PDF download and their answers:
Q1. From where can I download CBSE Class 11 Maths Ch 5 solutions PDF?
A. You can download all 11th Maths Ch 5 solutions from Embibe.
Q2. Are the CBSE 11th Maths solutions of Embibe available for free?
A. Yes, All solutions provided by Embibe are available for free. You don’t even have to sign up or register to download the solutions.
Q3. Is NCERT enough for Class 11 Maths?
A. For the annual exam of Class 11 Maths, NCERT Maths textbook and previous year papers are enough. For exams like JEE, you will have to refer to some advanced books as well.
|NCERT Solutions for Class 11 Maths Chapter 4||NCERT Solutions for Class 11 Maths Chapter 6||NCERT Solutions for Class 11 Maths (All Chapter)|
Important Questions And Terms In NCERT Solutions For Class 11 Maths Chapter 5
Below we have provided the summary and some important questions that will help you in preparing for the chapter:
|Important Notes on Complex Numbers|
a) Any number of the form y = p + iq, where p, q are real numbers, is known as a complex number. Where p is called the real part of y, denoted by Re(y) and q is called the imaginary part of y, denoted by Im(y).
b) x = 0 + i 0 is additive identity for a complex number.
c) –x = –p –iq is called the Additive Inverse or negative of x = p + iq.
d) a = 1 + i0 is multiplicative identity for complex number.
|Some Important Questions Chapter 5 Maths|
a) Express Z = -√3 +i in the polar form and also write the modulus and the argument of Z
b) Convert the following complex numbers in the polar form
i) 1 + i
ii) -1 + √3i
iii) -3 + 3i
c) Find the complex conjugate and multiplicative inverse of (2 – 5i)^2
d) Solve 2x^2 + 5 = 0
That was all the information on NCERT Solutions For Class 11 Maths Chapter 5 (Chapter 5 Maths Class 11 PDF download). Now that you have everything, start preparing for your exams.
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