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Class 11 Mathematics Complex Numbers And Quadratic Equation Assignments

We have provided below free printable Class 11 Mathematics Complex Numbers And Quadratic Equation Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 11 Mathematics Complex Numbers And Quadratic Equation . These Assignments for Grade 11 Mathematics Complex Numbers And Quadratic Equation cover all important topics which can come in your standard 11 tests and examinations. Free printable Assignments for CBSE Class 11 Mathematics Complex Numbers And Quadratic Equation , school and class assignments, and practice test papers have been designed by our highly experienced class 11 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Complex Numbers And Quadratic Equation Class 11 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Complex Numbers And Quadratic Equation Class 11. Students can click on the links below and download all Pdf Assignments for Mathematics Complex Numbers And Quadratic Equation class 11 for free. All latest Kendriya Vidyalaya Class 11 Mathematics Complex Numbers And Quadratic Equation Assignments with Answers and test papers are given below.

Mathematics Complex Numbers And Quadratic Equation Class 11 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 11 Mathematics Complex Numbers And Quadratic Equation . Students and teachers can download and save all free Mathematics Complex Numbers And Quadratic Equation assignments in Pdf for grade 11th. Our expert faculty have covered Class 11 important questions and answers for Mathematics Complex Numbers And Quadratic Equation as per the latest syllabus for the current academic year. All test papers and question banks for Class 11 Mathematics Complex Numbers And Quadratic Equation and CBSE Assignments for Mathematics Complex Numbers And Quadratic Equation Class 11 will be really helpful for standard 11th students to prepare for the class tests and school examinations. Class 11th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 11 Mathematics Complex Numbers And Quadratic Equation Download in Pdf

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Complex Numbers Class 11 Questions

Students will quickly understand the basics of the concept “Complex Numbers” with the aid of the complex numbers class 11 question s and answers. These questions can be used by students to briefly summarize the concept and we have also provided some practice problems so that they can comprehend the concept better. You can also get in-depth explanations for each question, and cross validate your answer as well. To learn more about complex numbers class 11, click here .

Complex Numbers Class 11 Questions with Solutions

1. Write the complex number i 9 + i 19 in the form of a + ib.

Given number: i 9 + i 19 .

The expression i 9 + i 19 can be represented as follows:

i 9 + i 19 = (i 2 ) 4 . i + (i 2 ) 9 . i …(1)

We know that, i 2 = 1.

On substituting i 2 = -1, we get

i 9 + i 19 = (-1) 4 .i + (-1) 9 .i

i 9 + i 19 = 1.i + (-1).i

i 9 + i 19 = i – i

i 9 + i 19 = 0.

Therefore, i 9 + i 19 in the form of a + ib is 0 + i0.

2. Simplify the expression: i 30 + i 40 + i 60 .

Given expression: i 30 + i 40 + i 60 .

The given expression can be simplified as follows:

i 30 + i 40 + i 60 = (i 4 ) 7 . i 2 + (i 4 ) 10 + (i 4 ) 15 .

We know that the value of i 4 is 1.

i 30 + i 40 + i 60 = (1) 7 . i 2 + (1) 10 + (1) 15 .

i 30 + i 40 + i 60 = (1)i 2 + 1 + 1

i 30 + i 40 + i 60 = 1

Therefore, the simplification of i 30 + i 40 + i 60 is 1.

3. Express the given expression (1 + i) (1 + 2i) in the form a + ib and find the values of a and b.

Given expression: (1 + i) (1 + 2i)

Hence, (1 + i) (1 + 2i) = 1(1) + 1(2i) + i + 2i(i)

(1 + i) (1 + 2i) = 1 + 2i + i + 2i 2

(1 + i) (1 + 2i) = 1 + 2i + i – 2

(1 + i) (1 + 2i) = -1 + 3i

Hence, the expression (1 + i) (1 + 2i) in the form of a + bi is -1 + 3i.

Thus, the value of a = -1 and b = 3.

4. Solve the equation: 2x 2 + x + 1 = 0

Given equation: 2x 2 + x + 1 = 0 …(1)

Now, compare the given equation with the standard quadratic equation ax 2 + bx + c = 0 …(b)

On comparing the equations (1) and (2), we get

a = 2, b = 1 and c = 1.

As we know discriminant, D = b 2 – 4ac …(3)

Substitute the values a, b and c in equation (3), we get

D = (1) 2 – 4(2)(1)

D = 1 – 8

We know that the quadratic equation formula is:

Now, the above equation can be written as

Since, √-1 = i,

Hence, the solutions to the given quadratic equation are:

5. Determine the multiplicative inverse of 4 – 3i.

Let z = 4 – 3i.

The conjugate of 4 – 3i is 4 + 3i.

As we know, the multiplicative inverse of z is 1/z.

Hence, 1/z = 1/ (4+3i)

Therefore, the multiplicative inverse of 4 – 3i is:

As, i 2 = -1

Therefore, the multiplicative inverse of 4 – 3i is (4 + 3i)/25.

6. If z 1 and z 2 are the two complex numbers, then show that Re (z 1 z 2 ) = Re z 1 Re z 2 – Im z 1 Im z 2 .

Let z 1 = a 1 + ib 1 and z 2 = a 2 + ib 2

Now, take the product of these two complex numbers.

z 1 z 2 = (a 1 + ib 1 )(a 2 + ib 2 )

z 1 z 2 = a 1 (a 2 + ib 2 ) + ib 1 (a 2 + ib 2 )

z 1 z 2 = a 1 a 2 + ia 1 b 2 + ia 2 b 1 + i 2 b 1 b 2

Now, the above equation can be rearranged as follows:

z 1 z 2 = a 1 a 2 – b 1 b 2 + ia 1 b 2 + ia 2 b 1

z 1 z 2 = (a 1 a 2 – b 1 b 2 ) + i(a 1 b 2 + a 2 b 1 )

Here, the real part is:

Re (z 1 z 2 ) = a 1 a 2 – b 1 b 2

Re (z 1 z 2 ) = Re z 1 Re z 2 – Im z 1 Im z 2 .

Hence, Re (z 1 z 2 ) = Re z 1 Re z 2 – Im z 1 Im z 2 is proved.

Also, read: Imaginary Numbers .

7. Determine the modulus and arguments of 1 – i. Also, find its polar form.

Given expression: 1 – i.

The complex number z = a + ib in polar form is given as z = |z| (cos θ + i sin θ) …(1)

Let z = 1 – i

Finding Modulus of 1 – i:

|z| = √(a 2 + b 2 )

|z| = √(1 2 + (-1) 2 )

|z| = √(1+1)

Hence, the modulus of 1 – i is √2.

Finding Argument of 1 – i:

θ = arg (z) = tan -1 (|b| / |a|)

Here, |b| = 1 and |a| = 1.

Hence, θ = arg (z) = tan -1 (1/1)

θ = arg (z) = tan -1 1

Now, substitute the values in (1), we get

Polar form, z = √2 (cos (-π/4) + i sin (-π/4))

z = √2 (cos (π/4) – i sin (π/4))

Therefore, the polar form of 1 – i is equal to √2 (cos (π/4) – i sin (π/4)).

8. Compute the value of (1-i) n [1- (1/i)] n for a positive integer “n”.

Given: (1 – i) n [1- (1/i)] n

We know that i 4 = 1,

Hence, (1 – i) n [1- (1/i)] n = (1 – i) n [1- (i 4 /i)] n

(1 – i) n [1- (1/i)] n = (1 – i) n [1 – i 3 ] n

Further, the above equation is written as follows:

(1 – i) n [1- (1/i)] n = [(1 – i) (1 + i)] n

The expression (1 – i) (1 + i) is of the form (a – b)(a + b), which is equal to a 2 – b 2 .

Here, a = 1, b = 1

Thus, (1 – i) n [1- (1/i)] n = (1 – i 2 ) n

(1 – i) n [1- (1/i)] n = (1 + 1) n

(1 – i) n [1- (1/i)] n = 2 n .

Therefore, the value of (1 – i) n [1- (1/i)] n is 2 n .

9. Solve the given equation: |z| = z + 1 + 2i.

Given equation: |z| = z + 1 + 2i.

Let z = a + ib

Hence, the given equation becomes:

|a + ib| = (a + ib) + 1 + 2i

√(a 2 + b 2 ) = (a + 1) + i (b + 2) …(1)

Now, compare the real and imaginary parts,

Real part: √(a 2 + b 2 ) = a + 1 …(2)

Imaginary part: 0 = b + 2

Hence, b = -2 …(3)

Now, substitute b = -2 in (2), we get

√(a 2 + (-2) 2 ) = a + 1

Now, take squares on both sides, we get

a 2 + 4 = (a+ 1) 2

a 2 + 4 = a 2 + 1 + 2a

2a = 4 – 1

Hence, a = 3/2 …(4)

Hence, the complex number, z = (3/2) -2i.

10. Show that arg (z 1 /z 4 ) + arg (z 2 /z 3 ) = 0, if z 1 , z 2 and z 3 and z 4 are the two pairs of conjugate complex numbers.

Given that,

As we know, arg (z 1 /z 2 ) = arg (z 1 ) – arg (z 2 )

Hence, (z 1 /z 4 ) + arg (z 2 /z 3 ) = arg (z 1 ) – arg (z 4 ) + arg (z 2 ) – arg (z 3 )

arg (z 1 /z 4 ) + arg (z 2 /z 3 ) = arg (z 1 ) + arg (z 2 ) – arg (z 4 ) – arg (z 3 )

Using (1) and (2), we can write

arg (z 1 /z 4 ) + arg (z 2 /z 3 ) = 0 – 0

arg (z 1 /z 4 ) + arg (z 2 /z 3 ) = 0

Hence, arg (z 1 /z 4 ) + arg (z 2 /z 3 ) = 0 is proved.

Explore More Questions

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Practice Questions

Solve the following complex numbers class 11 questions.

• Write the expression i -39 in the form of a + ib.
• Solve the equation: √2x 2 + x + √2 = 0.
• Write the given complex number in the polar form: (1 + 2i) / (1 – 3i).

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CBSE Worksheets for Class 11 Maths

CBSE Worksheets for Class 11 Maths: One of the best teaching strategies employed in most classrooms today is Worksheets. CBSE Class 11 Maths Worksheet for students has been used by teachers & students to develop logical, lingual, analytical, and problem-solving capabilities. So in order to help you with that, we at WorksheetsBuddy have come up with Kendriya Vidyalaya Class 11 Maths Worksheets for the students of Class 11. All our CBSE NCERT Class 11 Maths practice worksheets are designed for helping students to understand various topics, practice skills and improve their subject knowledge which in turn helps students to improve their academic performance. These chapter wise test papers for Class 11 Maths will be useful to test your conceptual understanding.

Board: Central Board of Secondary Education(www.cbse.nic.in) Subject: Class 11 Maths Number of Worksheets: 42

CBSE Class 11 Maths Worksheets PDF

All the CBSE Worksheets for Class 11 Maths provided in this page are provided for free which can be downloaded by students, teachers as well as by parents. We have covered all the Class 11 Maths important questions and answers in the worksheets which are included in CBSE NCERT Syllabus. Just click on the following link and download the CBSE Class 11 Maths Worksheet. CBSE Worksheets for Class 11 Math can also use like assignments for Class 11 Maths students.

Binomial Theorem

• CBSE Worksheets for Class 11 Mathematics Binomial Theorem Assignment 1
• CBSE Worksheets for Class 11 Mathematics Binomial Theorem Assignment 2

Complex Numbers and Quadratic Equation

• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 1
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 2
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 3
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 4
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 5
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 6

Conic Sections

• CBSE Worksheets for Class 11 Mathematics Conic Sections Assignment 1
• CBSE Worksheets for Class 11 Mathematics Conic Sections Assignment 2

Introduction To 3Dimensional Geometry

• CBSE Worksheets for Class 11 Mathematics Introduction To 3Dimensional Geometry Assignment 1
• CBSE Worksheets for Class 11 Mathematics Introduction To 3Dimensional Geometry Assignment 2

Linear Inequalities

• CBSE Worksheets for Class 11 Mathematics Linear Inequalities Assignment 1
• CBSE Worksheets for Class 11 Mathematics Linear Inequalities Assignment 2

Permutations and Combinations

• CBSE Worksheets for Class 11 Mathematics Permutations and Combinations Assignment 1
• CBSE Worksheets for Class 11 Mathematics Permutations and Combinations Assignment 2

Principle of Mathematical Induction

• CBSE Worksheets for Class 11 Mathematics Principle of Mathematical Induction Assignment 1
• CBSE Worksheets for Class 11 Mathematics Principle of Mathematical Induction Assignment 2

Probability

• CBSE Worksheets for Class 11 Mathematics Probability Assignment 1
• CBSE Worksheets for Class 11 Mathematics Probability Assignment 2

Relations and Functions

• CBSE Worksheets for Class 11 Mathematics Relations and Functions Assignment

Sequences and Series

• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 1
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 2
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 3
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 4
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 5
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 6
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 7
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 8
• CBSE Worksheets for Class 11 Mathematics Set Theory Assignment 1
• CBSE Worksheets for Class 11 Mathematics Set Theory Assignment 2
• CBSE Worksheets for Class 11 Mathematics Statistics Assignment 1
• CBSE Worksheets for Class 11 Mathematics Statistics Assignment 2

Straight Lines

• CBSE Worksheets for Class 11 Mathematics Straight Lines Assignment 1
• CBSE Worksheets for Class 11 Mathematics Straight Lines Assignment 2

Trigonometric Ratios

• CBSE Worksheets for Class 11 Mathematics Trigonometric Ratios Assignment 1
• CBSE Worksheets for Class 11 Mathematics Trigonometric Ratios Assignment 2
• CBSE Worksheets for Class 11 Mathematics Trigonometric Ratios Assignment 3
• CBSE Worksheets for Class 11 Mathematics Sample Paper 2014 Assignment 1
• CBSE Worksheets for Class 11 Mathematics Sample Paper 2014 Assignment 2
• CBSE Worksheets for Class 11 Mathematics Sample Paper 2014 Assignment 3
• CBSE Worksheets for Class 11 Mathematics Mathematical Reasoning Assignment

Advantages of CBSE Class 11 Maths Worksheets

• By practising NCERT CBSE Class 11 Maths Worksheet , students can improve their problem solving skills.
• Helps to develop the subject knowledge in a simple, fun and interactive way.
• No need for tuition or attend extra classes if students practise on worksheets daily.
• Working on CBSE worksheets are time-saving.
• Helps students to promote hands-on learning.
• One of the helpful resources used in classroom revision.
• CBSE Class 11 Maths Workbook Helps to improve subject-knowledge.
• CBSE Class 11 Math Worksheets encourages classroom activities.

Worksheets of CBSE Class 11 Maths are devised by experts of WorksheetsBuddy experts who have great experience and expertise in teaching Maths. So practising these worksheets will promote students problem-solving skills and subject knowledge in an interactive method. Students can also download CBSE Class 11 Maths Chapter wise question bank pdf and access it anytime, anywhere for free. Browse further to download free CBSE Class 11 Maths Worksheets PDF .

Now that you are provided all the necessary information regarding CBSE Class 11 Maths Worksheet and we hope this detailed article is helpful. So Students who are preparing for the exams must need to have great solving skills. And in order to have these skills, one must practice enough of Class 11 Math revision worksheets . And more importantly, students should need to follow through the worksheets after completing their syllabus.  Working on CBSE Class 11 Maths Worksheets will be a great help to secure good marks in the examination. So start working on Class 11 Math Worksheets to secure good score.

CBSE Worksheets For Class 11

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

Ncert solutions for class 11 maths chapter 5 – complex numbers and quadratic equations pdf.

Free PDF of NCERT Solutions for Class 11 Maths Chapter 5 – Complex Numbers and Quadratic Equations includes all the questions provided in NCERT Books prepared by Mathematics expert teachers as per CBSE NCERT guidelines from Mathongo.com. To download our free pdf of Chapter 5 – Complex Numbers and Quadratic Equations Maths NCERT Solutions for Class 11 to help you to score more marks in your board exams and as well as competitive exams.

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