MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. Multiple Choice Questions (MCQ) for Complex Numbers and Quadratic Equations - CBSE Class 11-science Mathematics on Topperlearning. So, x2000 + 1/x2000 = -1, Question 17. Download JEE Mathematics Complex Numbers MCQs Set A in pdf, Complex Numbers chapter wise Multiple Choice Questions free Hint: Given, (3y – 2) + i(7 – 2x) = 0 ⇒ 4sin² θ = 3 This contains 30 Multiple Choice Questions for JEE Test: Complex Numbers (mcq) to study with solutions a complete question bank. MCQ from maths chapter Complex numbers. (b) -12i So, the modulus of 5 + 4i is √41. (c) 23n The solved questions answers in this Test: Complex Numbers quiz give you a good mix of easy questions and tough questions. (c) 17i (b) 2 Complex Numbers ML Aggarwal ISC Class-11 Maths Understanding Solutions Chapter-5. (c) x = 7/2, y = 3/2 = w2000 + 1/w2000 These short solved questions or quizzes are provided by Gkseries. = √(-1) × √(25) + 3{√(-1) × √4} + 2{√(-1) × √9} (b) θ = nπ ± π/3 where n is an integer Given, (c) √41 = [{(1 + i) × (1 + i)}/{(1 – i) × (1 + i)}]n (c) -2i Let z be a complex number such that |z| = 4 and arg(z) = 5π/6, then z = (b) 2√3 + 2i Provide me latest MCQ Questions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Free PDF Download so I can prepare for exams. Now both of them are not possible for the same value of x. Answer: (a) a circleHint:Let w = 2/zNow, |w| = |2/z|=> |w| = 2/|z|=> |w| = 2This shows that w lies on a circle with center at the origin and radius 2 units. (b) -12i The value of i-999 is Question 1.The value of √(-16) is(a) -4i(b) 4i(c) -2i(d) 2i, Answer: (b) 4iHint:Given, √(-16) = √(16) × √(-1)= 4i {since i = √(-1) }, Question 2.The value of √(-144) is(a) 12i(b) -12i(c) ±12i(d) None of these, Answer: (a) 12iHint:Given, √(-144) = √{(-1) × 144}= √(-1) × √(144)= i × 12 {Since √(-1) = i}= 12iSo, √(-144) = 12i, Question 3:The value of √(-25) + 3√(-4) + 2√(-9) is(a) 13i(b) -13i(c) 17i(d) -17i, Answer: (c) 17iHint:Given, √(-25) + 3√(-4) + 2√(-9)= √{(-1) × (25)} + 3√{(-1) × 4} + 2√{(-1) × 9}= √(-1) × √(25) + 3{√(-1) × √4} + 2{√(-1) × √9}= 5i + 3×2i + 2×3i {since √(-1) = i}= 5i + 6i + 6i= 17iSo, √(-25) + 3√(-4) + 2√(-9) = 17i, Question 4.if z lies on |z| = 1, then 2/z lies on(a) a circle(b) an ellipse(c) a straight line(d) a parabola. = w² + w This chapter provides detailed information about the complex numbers and how to represent complex numbers in the Arg and plane. (c) i = (2² w³)×(2² w³)×(2² w³) …………… to 2n factors The value of √(-16) is (d) -i, Answer: (c) i The questions are from. (b) -41 (d) 2i, Answer: (b) 4i Further assume that the origin, z1 and z1 form an equilateral triangle. (a) x = 7/2, y = 2/3 ⇒ (1 + ω – ω2)7 = -128 ω14 The curve represented by Im(z²) = k, where k is a non-zero real number, is ⇒ (1 + ω – ω2)7 = -128 ω12 × ω2 Now, z² = (x + iy)² |Z| = √(5² + 4²) (c) 2√3 – 2i (c) -π/2 CBSE Guide Complex Numbers And Quadratic Equations class 11 Notes. = 4i {since i = √(-1) }, Question 2. You will be able to view the results only after attempting all the questions. ⇒ [(1 + i² + 2i)/{1 – (-1)}]n = 1 ⇒ [(1 – 1 + 2i)/{1 + 1}]n = 1 So, i-999 = i, Question 9. which has roots, by the Quadratic Formula, to be u = 1 ± i√3 11+12 – Physics; ... > MCQ from maths chapter Complex numbers. (b) 22n Let Z = 5 + 4i Given, √(-16) = √(16) × √(-1) MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. Hint: Hint: Complex Numbers and Quadratic Equations Class 11 MCQs Questions with Answers. Register online for Maths tuition on Vedantu.com to … Given, Im(z²) = k (d) x = 2/7, y = 3/2, Answer: (a) x = 7/2, y = 2/3 x² + x + 1 = 0 (3 + 2i × sin θ)/(1 – 2i × sin θ) = {(3 – 4sin² θ) + 8i × sin θ}/(1 + 4sin² θ) …………. (b) 1 11+12 – Physics; 11+12 – Chemistry; 11+12 – Mathematics; 11 – Physics; 11 – Chemistry; 11 – Mathematics; Class 12. = 1/(i996 × i³) All questions, including examples and miscellaneous have been solved and divided into different Concepts, with questions ordered from easy to difficult.The topics of the chapter includeSolvingQuadratic equationwhere root is in negativ CBSE Class 11th Math 5 – Complex Numbers and Quadratic Equations MCQs If α and β are the roots of the equation 3 x 2 + 2x + 7 = 0, then 1/α+1/β=____. 1Now, equation 1 is imaginary if3 – 4sin² θ = 0⇒ 4sin² θ = 3⇒ sin² θ = 3/4⇒ sin θ = ±√3/2⇒ θ = nπ ± π/3 where n is an integer, Question 14.If {(1 + i)/(1 – i)}n = 1 then the least value of n is(a) 1(b) 2(c) 3(d) 4, Answer: (d) 4Hint:Given, {(1 + i)/(1 – i)}n = 1⇒ [{(1 + i) × (1 + i)}/{(1 – i) × (1 + i)}]n = 1⇒ [{(1 + i)²}/{(1 – i²)}]n = 1⇒ [(1 + i² + 2i)/{1 – (-1)}]n = 1⇒ [(1 – 1 + 2i)/{1 + 1}]n = 1⇒ [2i/2]n = 1⇒ in = 1Now, in is 1 when n = 4So, the least value of n is 4, Question 15.If arg (z) < 0, then arg (-z) – arg (z) =(a) π(b) -π(c) -π/2(d) π/2, Answer: (a) πHint:Given, arg (z) < 0Now, arg (-z) – arg (z) = arg(-z/z)⇒ arg (-z) – arg (z) = arg(-1)⇒ arg (-z) – arg (z) = π {since sin π + i cos π = -1, So arg(-1) = π}, Question 16.if x + 1/x = 1 find the value of x2000 + 1/x2000 is(a) 0(b) 1(c) -1(d) None of these, Answer: (c) -1Hint:Given x + 1/x = 1⇒ (x² + 1) = x⇒ x² – x + 1 = 0⇒ x = {-(-1) ± √(1² – 4 × 1 × 1)}/(2 × 1)⇒ x = {1 ± √(1 – 4)}/2⇒ x = {1 ± √(-3)}/2⇒ x = {1 ± √(-1)×√3}/2⇒ x = {1 ± i√3}/2 {since i = √(-1)}⇒ x = -w, -w²Now, put x = -w, we getx2000 + 1/x2000 = (-w)2000 + 1/(-w)2000= w2000 + 1/w2000= w2000 + 1/w2000= {(w³)666 × w²} + 1/{(w³)666 × w²}= w² + 1/w² {since w³ = 1}= w² + w³ /w²= w² + w= -1 {since 1 + w + w² = 0}So, x2000 + 1/x2000 = -1, Question 17.The value of √(-144) is(a) 12i(b) -12i(c) ±12i(d) None of these, Answer: (a) 12iHint:Given, √(-144) = √{(-1)×144}= √(-1) × √(144)= i × 12 {Since √(-1) = i}= 12iSo, √(-144) = 12i, Question 18.If the cube roots of unity are 1, ω, ω², then the roots of the equation (x – 1)³ + 8 = 0 are(a) -1, -1 + 2ω, – 1 – 2ω²(b) – 1, -1, – 1(c) – 1, 1 – 2ω, 1 – 2ω²(d) – 1, 1 + 2ω, 1 + 2ω², Answer: (c) – 1, 1 – 2ω, 1 – 2ω²Hint:Note that since 1, ω, and ω² are the cube roots of unity (the three cube roots of 1), they are the three solutions to x³ = 1 (note: ω and ω² are the two complex solutions to this)If we let u = x – 1, then the equation becomesu³ + 8 = (u + 2)(u² – 2u + 4) = 0.So, the solutions occur when u = -2 (giving -2 = x – 1 ⇒ x = -1), or when:u² – 2u + 4 = 0,which has roots, by the Quadratic Formula, to be u = 1 ± i√3So, x – 1 = 1 ± i√3⇒ x = 2 ± i√3Now, x³ = 1 when x³ – 1 = (x – 1)(x² + x + 1) = 0, giving x = 1 andx² + x + 1 = 0⇒ x = (-1 ± i√3)/2If we let ω = (-1 – i√3)/2 and ω₂ = (-1 + i√3)/2then 1 – 2ω and 1 – 2ω² yield the two complex solutions to (x – 1)³ + 8 = 0So, the roots of (x – 1)³ + 8 are -1, 1 – 2ω, and 1 – 2ω², Question 19. ⇒ (1 + ω – ω2)7 = -128 (ω3)4 ω2 There will be total 15 MCQ in this test. (a) 12i Hint: 4. Hint: (1) By equating the real and the imaginary parts of equation (1), 4x = 3, 3x – y = –6, Now, 4x = 3. = 12i Answer. = w² + w³ /w² Question 5. = in Complex Numbers Class 11 – A number that can be represented in form p + iq is defined as a complex number. ⇒ x = 3/4. The test consists 25 questions. = -1 {since 1 + w + w² = 0} Given x + 1/x = 1 (d) -17i, Answer: (c) 17i Given, √(-25) + 3√(-4) + 2√(-9) Given, z1 and z2 be two roots of the equation z² + az + b = 0 (a) θ = nπ ± π/2 where n is an integer Question 12.The value of x and y if (3y – 2) + i(7 – 2x) = 0(a) x = 7/2, y = 2/3(b) x = 2/7, y = 2/3(c) x = 7/2, y = 3/2(d) x = 2/7, y = 3/2, Answer: (a) x = 7/2, y = 2/3Hint:Given, (3y – 2) + i(7 – 2x) = 0Compare real and imaginary part, we get3y – 2 = 0⇒ y = 2/3and 7 – 2x = 0⇒ x = 7/2So, the value of x = 7/2 and y = 2/3, Question 13.Find real θ such that (3 + 2i × sin θ)/(1 – 2i × sin θ) is imaginary(a) θ = nπ ± π/2 where n is an integer(b) θ = nπ ± π/3 where n is an integer(c) θ = nπ ± π/4 where n is an integer(d) None of these, Answer: (b) θ = nπ ± π/3 where n is an integerHint:Given,(3 + 2i × sin θ)/(1 – 2i × sin θ) = {(3 + 2i × sin θ)×(1 – 2i × sin θ)}/(1 – 4i² × sin² θ)(3 + 2i × sin θ)/(1 – 2i × sin θ) = {(3 – 4sin² θ) + 8i × sin θ}/(1 + 4sin² θ) …………. = 22n, Question 20. Class 11 Maths MCQs Questions with Answers Chapter Wise PDF Download. If you have any queries regarding CBSE Class 11 Maths Complex Numbers and Quadratic Equations MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon. ⇒ x = 7/2 Hindi Mathematics. Provide me latest MCQ Questions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Free PDF Download so I can prepare for exams. (a) (b) p. (c) … (b) an ellipse There will be total 15 MCQ in this test. Check the below NCERT MCQ Questions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations with Answers Pdf free download. The exemplar questions constitute of variety of questions such as Multiple-Choice Questions (MCQs), Short Answer Questions (SA) and Long Answer Questions (LA). Complex Number can be considered as the super-set of all the other different types of number. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. = √{(-1) × (25)} + 3√{(-1) × 4} + 2√{(-1) × 9} शिक्षण प्रक्रिया में शिक्षक को अनेक कार्य एक साथ करने पड़ते हैं जैसे लिखना, प्रश्न पूछना, स्पष्ट करना, प्रदर्शन करना... शिक्षण कौशल ( Teaching Skill) ⇒ tan x = 1 and tan 2x = 1 Answer: (a) a circle Complex Numbers and Quadratic Equations Class 11 NCERT Book: If you are looking for the best books of Class 11 Maths then NCERT Books can be a great choice to begin your preparation. ⇒ x = {-(-1) ± √(1² – 4 × 1 × 1)}/(2 × 1) MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. 3210 views June 24, 2018 Class 11, 12 - Maths. This mock test of Test: Complex Numbers for JEE helps you for every JEE entrance exam. Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. ⇒ z = -2√3 + 2i, Question 8: Chapter 7 Class 11 … MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. Class 11 Maths Formulas: Complex Numbers And Quadratic Equations. Question 5.If ω is an imaginary cube root of unity, then (1 + ω – ω²)7 equals(a) 128 ω(b) -128 ω(c) 128 ω²(d) -128 ω², Answer: (d) -128 ω²Hint:Given ω is an imaginary cube root of unity.So 1 + ω + ω² = 0 and ω³ = 1Now, (1 + ω – ω²)7 = (-ω² – ω²)7⇒ (1 + ω – ω2)7 = (-2ω2)7⇒ (1 + ω – ω2)7 = -128 ω14⇒ (1 + ω – ω2)7 = -128 ω12 × ω2⇒ (1 + ω – ω2)7 = -128 (ω3)4 ω2⇒ (1 + ω – ω2)7 = -128 ω2, Question 6.The least value of n for which {(1 + i)/(1 – i)}n is real, is(a) 1(b) 2(c) 3(d) 4, Answer: (b) 2Hint:Given, {(1 + i)/(1 – i)}n= [{(1 + i) × (1 + i)}/{(1 – i) × (1 + i)}]n= [{(1 + i)²}/{(1 – i²)}]n= [(1 + i² + 2i)/{1 – (-1)}]n= [(1 – 1 + 2i)/{1 + 1}]n= [2i/2]n= inNow, in is real when n = 2 {since i2 = -1 }So, the least value of n is 2, Question 7.Let z be a complex number such that |z| = 4 and arg(z) = 5π/6, then z =(a) -2√3 + 2i(b) 2√3 + 2i(c) 2√3 – 2i(d) -√3 + i, Answer: (a) -2√3 + 2iHint:Let z = r(cos θ + i × sin θ)Then r = 4 and θ = 5π/6So, z = 4(cos 5π/6 + i × sin 5π/6)⇒ z = 4(-√3/2 + i/2)⇒ z = -2√3 + 2i, Question 8:The value of i-999 is(a) 1(b) -1(c) i(d) -i, Answer: (c) iHint:Given, i-999= 1/i999= 1/(i996 × i³)= 1/{(i4)249 × i3}= 1/{1249 × i3} {since i4 = 1}= 1/i3= i4/i3 {since i4 = 1}= iSo, i-999 = i, Question 9.Let z1 and z2 be two roots of the equation z² + az + b = 0, z being complex. Brief Discussion on Sets Part - … Questions with Answers Question 1 Add and express in the form of a complex number a + b i. ⇒ |Z| = √41 (c) a parabola Here you can get Class 11 Important Questions Maths based on NCERT Text book for Class XI. CBSE Class 11th Math 5 – Complex Numbers and Quadratic Equations MCQs. Answer: (d) a hyperbolaHint:Let z = x + iyNow, z² = (x + iy)²⇒ z² = x² – y² + 2xyGiven, Im(z²) = k⇒ 2xy = k⇒ xy = k/2 which is a hyperbola. Hint: Free PDF download of RD Sharma Class 11 Solutions Chapter 13 - Complex Numbers Exercise 13.3 solved by Expert Mathematics Teachers on Vedantu.com. => |w| = 2/|z| For positive integers n1, n2 the value of expression + here is a real number, if and only if. Complex Numbers and Quadratic Equations Class 11 MCQs Questions with Answers. Click here to join our FB Page and FB Group for Latest update and preparation tips and queries. Hint: 11+12 – Physics; 11+12 – Chemistry; 11+12 – Mathematics; 11 – Physics; ... > Multiple Choice Questions from chapter 5 complex numbers. u³ + 8 = (u + 2)(u² – 2u + 4) = 0. The least value of n for which {(1 + i)/(1 – i)}n is real, is = [(1 + i² + 2i)/{1 – (-1)}]n = 5i + 6i + 6i Hint: Chapter 6 Class 11 Linear Inequalities. Given complex number = sin x + i cos 2x (a) 1 (a) 12i Now, in is real when n = 2 {since i2 = -1 } (c) θ = nπ ± π/4 where n is an integer These MCQ's are extremely critical for all CBSE students to score better marks. Hint: ⇒ z = 4(-√3/2 + i/2) NCERT Books for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations can be of extreme use for students to understand the concepts in a simple way.Class 11th Maths NCERT Books … If you have any queries regarding CBSE Class 11 Maths Complex Numbers and Quadratic Equations MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon. ⇒ z12+ z22 = z1 × z2 {since z3 = 0} u² – 2u + 4 = 0, (b) -1 Introduction to Complex Numbers, Class 11 Mathematics NCERT Solutions. What are Complex Numbers? ⇒ z12 + z22 + z32 = z1 × z2 + z2 × z3 + z1 × z3 Given, i-999 Anuj Seth. ⇒ (z1 + z2)² = 3z1 × z2 Then r = 4 and θ = 5π/6 For your final exams, Ncert Maths Exemplar for class 11 can help you a lot in order to prepare. Given, √(-144) = √{(-1)×144} Note that since 1, ω, and ω² are the cube roots of unity (the three cube roots of 1), they are the three solutions to x³ = 1 (note: ω and ω² are the two complex solutions to this) Given Complex number: (1 – i) … Class 11 Mathematics notes on Chapter 5 Complex Numbers And Quadratic Equations class 11 Notes Mathematics are also available for download in CBSE Guide website. So, the least value of n is 2, Question 7. = i × 12 {Since √(-1) = i} Chapter 5 Class 11 Complex Numbers. we will cover this topic from basic also we will try to solve MCQ based on chapter. If the cube roots of unity are 1, ω, ω², then the roots of the equation (x – 1)³ + 8 = 0 are If z1, z2 and z3, z4 are two pairs of conjugate complex numbers then. Given, √(-144) = √{(-1) × 144} The above NCERT CBSE and KVS worksheets for Class 11 Complex Numbers and Quadratic Equation will help you to improve marks by clearing Complex Numbers and Quadratic Equation concepts and also improve problem solving skills. Question 1. All Chapter-13 Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. Chapter 11 Class 11 Conic Sections. (a) -2√3 + 2i 0. 1 (d) 4, Answer: (d) 4 (c) ±12i Check the below NCERT MCQ Questions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations with Answers Pdf free download. = [(1 – 1 + 2i)/{1 + 1}]n 0. ⇒ sin² θ = 3/4 ⇒ [2i/2]n = 1 complex number. 3 – 4sin² θ = 0 Now, in is 1 when n = 4 ⇒ x² – x + 1 = 0 302k watch mins. (d) a hyperbola. ⇒ x = {1 ± i√3}/2 {since i = √(-1)} Ended on Jun 25, 2020. Let z = x + iy (c) 3 Question 1. Complex numbers Ex 13.1 Q1(i) Complex numbers Ex 13.1 Q1(ii) Complex numbers Ex 13.1 Q1(iii) Complex numbers Ex 13.1 Q1(iv) Complex numbers Ex 13.1 Q1(v) This test is Rated positive by 87% students preparing for JEE.This MCQ test is related to JEE syllabus, prepared by JEE teachers. Further assume that the origin, z1 and z1 form an equilateral triangle. The value of √(-144) is So, the least value of n is 4, Question 15. (a) 128 ω . ⇒ 2xy = k (a) x = nπ (d) -128 ω², Answer: (d) -128 ω² Let z = r(cos θ + i × sin θ) These MCQ's are extremely critical for all CBSE students to score better marks. = i × 12 {Since √(-1) = i} This mock test of Test: Complex Numbers for JEE helps you for every JEE entrance exam. These questions unlike CBSE Ncert Textbook are a bit more difficult as well as advanced. If we let u = x – 1, then the equation becomes Now, (1 + ω – ω²)7 = (-ω² – ω²)7 (c) a² = 3b So, z = 4(cos 5π/6 + i × sin 5π/6) (c) ±12i ⇒ (x² + 1) = x 1. (b) -13i Complex Numbers Class 11 - CBSE - Quick concepts and MCQs in this course we will study basics and concepts of class 11 CBSE complex number . = (2²)n {since w³ = 1} So, there exist no value of x, Question 11. Given, {(1 + i)/(1 – i)}n = 1 (a) 0 Class 11 maths NCERT solutions state that there is a number root over -1. Given ω is an imaginary cube root of unity. Let w = 2/z (d) None of these, Answer: (c) -1 => |w| = 2 = 12i You may Re-attempt the test any number of times. (d) no value of x, Answer: (d) no value of x = w² + 1/w² {since w³ = 1} Visit official Website CISCE for detail information about ISC Board Class-11 Mathematics. The modulus of 5 + 4i is (b) 4i These CBSE NCERT Class 11 Complex Numbers and Quadratic Equation workbooks and question banks have been made by teachers of StudiesToday for benefit of Class 11 … Step by step Solutions of ML Aggarwal ISC Class-11 Mathematics with Exe1.1, Exe-1.2, Exe-1.3, Exe-1.4, Exe-1.5, Exe-1.6, Exe-1.7, and Chapter Test Questions. (a) -4i ⇒ [{(1 + i) × (1 + i)}/{(1 – i) × (1 + i)}]n = 1 Share. We have provided Complex Numbers and Quadratic Equations Class 11 Maths MCQs Questions with Answers to help students understand the concept very well. Hint: If arg (z) < 0, then arg (-z) – arg (z) = Register for online coaching for IIT JEE (Mains & Advanced), NEET, Engineering and Medical entrance exams. ⇒ x = 2 ± i√3 ⇒ (z1 + z2)² = 2z1 × z2 + z1 × z2 Multiple Choice Questions (MCQ) for CBSE Class 11-science Mathematics chapters on Topperlearning. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number. Hint: ⇒ arg (-z) – arg (z) = arg(-1) 1. Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. (a) a² = b Introduction to Complex Numbers, Class 11 Mathematics NCERT Solutions. These MCQ's are extremely critical for all CBSE students to score better marks. 3y – 2 = 0 = 1/{(i4)249 × i3} Given, {(1 + i)/(1 – i)}n ⇒ x = (-1 ± i√3)/2 We hope the given NCERT MCQ Questions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations with Answers Pdf free download will help you. (a) a circle Chapter 7 Class 11 Permutations and Combinations. if z lies on |z| = 1, then 2/z lies on For a complex number z = p + iq, p is known as the real part, represented by Re z and q is known as the imaginary part, it is represented by Im z of complex number z. No negative marking for incorrect choice. KPK MCQs Hint: (a) 13i ⇒ (-a)² = 3b = √(-1) × √(144) Now, equation 1 is imaginary if So, the roots of (x – 1)³ + 8 are -1, 1 – 2ω, and 1 – 2ω², Question 19. Compare real and imaginary part, we get The value of √(-144) is = (1 – w + w2)×(1 – w2 + w )×(1 – w + w2) × …………… to 2n factors (b) x = 2/7, y = 2/3 (1 – w + w²)×(1 – w² + w4)×(1 – w4 + w8) × …………… to 2n factors is equal to(a) 2n(b) 22n(c) 23n(d) 24n, Answer: (b) 22nHint:Given, (1 – w + w²)×(1 – w² + w4)×(1 – w4 + w8) × …………… to 2n factors= (1 – w + w2)×(1 – w2 + w )×(1 – w + w2) × …………… to 2n factors{Since w4 = w, w8 = w2}= (-2w) × (-2w²) × (-2w) × (-2w²)× …………… to 2n factors= (2² w³)×(2² w³)×(2² w³) …………… to 2n factors= (2²)n {since w³ = 1}= 22n, Question 20.The modulus of 5 + 4i is(a) 41(b) -41(c) √41(d) -√41, Answer: (c) √41Hint:Let Z = 5 + 4iNow modulus of Z is calculated as|Z| = √(5² + 4²)⇒ |Z| = √(25 + 16)⇒ |Z| = √41So, the modulus of 5 + 4i is √41. ⇒ x = {1 ± √(-1)×√3}/2 RD Sharma Solutions , RS Aggarwal Solutions and NCERT Solutions. शिक्षण प्रक्रिया में शिक्षक को अनेक कार्य एक साथ करने पड़ते हैं जैसे लिखना, प्रश्न पूछना, स्पष्ट करना, प्रदर्शन करना... शिक्षण कौशल ( Teaching Skill) Question 1. (a) 41 Hint: It goes to show that it is a solution to the equation x 2 +1=0. Multiple Choice Questions from chapter 5 complex numbers. Hint: ⇒ x = {1 ± √(-3)}/2 11TH CLASS MCQs on complex number. Parshant Kumar. and 7 – 2x = 0 Free PDF download of Important Questions with solutions for CBSE Class 11 Maths Chapter 5 - Complex Numbers and Quadratic Equations prepared by expert Maths teachers from latest edition of CBSE(NCERT) books. 2/7 (c) – 1, 1 – 2ω, 1 – 2ω² Similar Classes. CBSE Class 6 Mathematics Worksheets /Part 5 /Half Yearly Examination. Since z1 and z2 and z3 from an equilateral triangle. Hint: Given, arg (z) < 0 ⇒ (1 + ω – ω2)7 = (-2ω2)7 = i If {(1 + i)/(1 – i)}n = 1 then the least value of n is Now, x³ = 1 when x³ – 1 = (x – 1)(x² + x + 1) = 0, giving x = 1 and The value of x and y if (3y – 2) + i(7 – 2x) = 0 The questions includes 1 mark questions, 2 mark questions, 3 mark questions, 4 mark questions, 5 mark questions and other questions as per the latest CBSE curriculum for the current session. Write the given complex number (1 – i) – ( –1 + i6) in the form a + ib. 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