NCERT Solutions for Class 11 Maths Chapter 5: Complex Numbers and Quadratic Equations

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NCERT Solutions for class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations are given in the article. A complex number is a number that can be written as a+ib. A quadratic equation is a polynomial with two roots or a degree of two. A quadratic equation has the general form y=ax²+bx+c.

NCERT Solutions for class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations cover important concepts including a detailed introduction to Complex Numbers, Algebra of Complex Equations, Modulus & Conjugate of a Complex Number, Argand Plane and Polar Representation.

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Class 11 Maths NCERT Solutions Chapter 5 Complex Numbers and Quadratic Equations

Class 11 Maths NCERT Solutions Chapter 5 Complex Numbers and Quadratic Equations are provided below:

NCERT Solutions Mathematics

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Important Topics for Class 11 Maths NCERT Solutions Chapter 5 Complex Numbers & Quadratic Equations

Important Topics for Class 11 Maths NCERT Solutions Chapter 5 Complex Numbers & Quadratic Equations are elaborated below:

Addition of two complex numbers

The sum of two imaginary numbers is imaginary (unless it is 0). Set of numbers that solve equations of the form x² = (a negative real number) is called the set of imaginary numbers.

Formula used to add complex numbers is:

(a + ib) + (c + id) = (a + c) + i(b + d)

How to Add Complex Numbers: Step by Step Guide

Step 1: Change all imaginary numbers to bi form.

Step 2: Add the real parts of complex numbers.

Step 3: Add the imaginary parts of complex numbers.

Step 4: Write the answer in the form a + bi.

Difference of two complex numbers

Difference of two complex numbers is calculated using the formula:

(a + ib) - (c + id) = (a - c) + i(b - d)

Example: Subtract the complex numbers -12 + 6i and 7 + 5i.

Solution: Using the formula (a + ib) - (c + id) = (a - c) + i(b - d)

Here a = -12, b = 6, c = 7, d = 5

(-12 + 6i) - (7 + 5i) = (-12 - 7) + i(6 - 5)

= -19 + i

= (-12 + 6i) - (7 + 5i) = -19 + i

Multiplication of two complex numbers

Difference of two complex numbers is calculated using the formula:

(a + ib) (c + id) = (ac - bd) + i(ad + bc)

How to Multiply Complex Numbers: Step by Step Guide

Step 1: Apply distributive property and multiply each term of the first complex number with each term of the second complex number.

Step 2: Simplify i² = -1

Step 3: Combine real parts and imaginary parts and then simplify them to get the product.

Division of two complex numbers

Division of complex numbers is done by finding a term by which the numerator and the denominator can be multiplied. This would eliminate the imaginary part of the denominator so that the end product has a real number in the denominator.

How to Multiply Complex Numbers: Step by Step Guide

Step 1: First, calculate the conjugate of the complex number that is at the denominator of the fraction.

Step 2: Multiply the conjugate with the numerator and the denominator of the complex fraction.

Step 3: Apply the algebraic identity (a+b)(a-b)=a² - b² in the denominator and substitute i² = -1.

Step 4: Apply the distributive property in the numerator and simplify.

Step 5: Separate the real part and the imaginary part of the resultant complex number.

Argand Plane and Polar Representation

Argand plane is similar to coordinate plane, and the x-axis is the real part of the complex number, and the y-axis represents imaginary part of the complex number.

Complex number z = x + iy is represented as the point (x, y) and it can also be represented in polar form with its polar coordinates.

NCERT Solutions For Class 11 Maths Chapter 5 Exercises:

The detailed solutions for all the NCERT Solutions for Chapter 5 Complex Numbers and Quadratic Equations under different exercises are as follows:

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1.
If (i) A=\(\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}\),then verify that A'A=I
(ii) A= \(\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}\),then verify that A'A=I

View Solution

2.
Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)ⁿ=aⁿI+na^n-1bA,where I is the identity matrix of order 2 and n∈N

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3.
Find the inverse of each of the matrices,if it exists \(\begin{bmatrix} 2 & 1 \\ 7 & 4 \end{bmatrix}\)

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4.
Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}\)

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5.
Let f: R→R be defined as f(x) = 3x. Choose the correct answer.

f is one-one onto
f is many-one onto
f is one-one but not onto
f is neither one-one nor onto

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6.
Find the following integral: \(\int (ax^2+bx+c)dx\)

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NCERT Solutions for Class 11 Maths Chapter 5: Complex Numbers and Quadratic Equations

Class 11 Maths NCERT Solutions Chapter 5 Complex Numbers and Quadratic Equations

Important Topics for Class 11 Maths NCERT Solutions Chapter 5 Complex Numbers & Quadratic Equations

NCERT Solutions For Class 11 Maths Chapter 5 Exercises:

CBSE CLASS XII Related Questions

1.
If (i) A=\(\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}\),then verify that A'A=I
(ii) A= \(\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}\),then verify that A'A=I

2.
Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)ⁿ=aⁿI+na^n-1bA,where I is the identity matrix of order 2 and n∈N

3.
Find the inverse of each of the matrices,if it exists \(\begin{bmatrix} 2 & 1 \\ 7 & 4 \end{bmatrix}\)

4.
Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}\)

5.
Let f: R→R be defined as f(x) = 3x. Choose the correct answer.

6.
Find the following integral: \(\int (ax^2+bx+c)dx\)

Similar Mathematics Concepts

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NCERT Solutions for Class 11 Maths Chapter 5: Complex Numbers and Quadratic Equations

Class 11 Maths NCERT Solutions Chapter 5 Complex Numbers and Quadratic Equations

Important Topics for Class 11 Maths NCERT Solutions Chapter 5 Complex Numbers & Quadratic Equations

NCERT Solutions For Class 11 Maths Chapter 5 Exercises:

CBSE CLASS XII Related Questions

1. If (i) A=\(\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}\),then verify that A'A=I(ii) A= \(\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}\),then verify that A'A=I

2. Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)n=anI+nan-1bA,where I is the identity matrix of order 2 and n∈N

3. Find the inverse of each of the matrices,if it exists \(\begin{bmatrix} 2 & 1 \\ 7 & 4 \end{bmatrix}\)

4. Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}\)

5. Let f: R→R be defined as f(x) = 3x. Choose the correct answer.

6. Find the following integral: \(\int (ax^2+bx+c)dx\)

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
If (i) A=\(\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}\),then verify that A'A=I
(ii) A= \(\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}\),then verify that A'A=I

2.
Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)ⁿ=aⁿI+na^n-1bA,where I is the identity matrix of order 2 and n∈N

3.
Find the inverse of each of the matrices,if it exists \(\begin{bmatrix} 2 & 1 \\ 7 & 4 \end{bmatrix}\)

4.
Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}\)

5.
Let f: R→R be defined as f(x) = 3x. Choose the correct answer.

6.
Find the following integral: \(\int (ax^2+bx+c)dx\)