h &� CJ UVaJ j h &� UhH h &� # 4 5 8 : @ A ] ^ a y � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � d. 0 �. It is reflects Algebra 2 (algebra ii) level exercises. . 3 - (-2+3i) + (-5+i) = ? These MCQ's are extremely critical for all CBSE students to score better marks. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. � : . This is a multiple choice question (MCQ) quiz. a) Find b and c b) Write down the second root and check it. You can also have online access to Engineering Maths Multiple Choice Questions Answers EBook. Provide an appropriate response. � � s+ � � � �- : @ 0�v��� t ^ ?, . Multiple Choice Questions (MCQ) for CBSE Class 11-science Mathematics chapters on Topperlearning. 1 -1 Name the complex number represented on the complex plane: (3,2) 2 + 3i. 3 + 2i. 1. ... Then multiply the number by its complex conjugate. 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. 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. Questions on Complex Numbers . Values but not cell references b. EMBED Equation.3 34 5 7 -34 2. a. � � : : N. � � � : : � : � : . Title: Complex Numbers Quiz 2 Author: cmitchell Last modified by: cmitchell Created Date: 11/1/2010 8:29:00 PM Company: mvusd Other titles: Below is a set of multiple-choice questions and constructed-response questions that are similar to the questions you will see on Subtest I of CSET: Mathematics. Read and attempt to answer every question … Test your understanding of Complex numbers concepts with Study.com's quick multiple choice quizzes. b. 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. 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. i = - 1 1) A) True B) False Write the number as a product of a real number and i. Simplify the radical expression. Practice the multiple choice questions to test understanding of important topics in the chapters. Find the product of 4 + i and 4 � i 15 17 EMBED Equation.3 16 4. शिक्षण प्रक्रिया में शिक्षक को अनेक कार्य एक साथ करने पड़ते हैं जैसे लिखना, प्रश्न पूछना, स्पष्ट करना, प्रदर्शन करना... शिक्षण कौशल ( Teaching Skill) Missed a question here and there? h &� CJ UVaJ j h &� h &� EH��UjQ@yP 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. h &� CJ UVaJ j� h &� h &� EH��Uj�@yP Click here to join our FB Page and FB Group for Latest update and preparation tips and queries. Select the correct answer and submit. Start below. Further assume that the origin, z1 and z1 form an equilateral triangle. Perform the operation and write the result in standard form. You will see that, in general, you proceed as in real numbers, but using i 2 =−1 where appropriate. Find all complex numbers z such that z 2 = -1 + 2 sqrt(6) i. EMBED Equation.3 i -i 1 -1 Name the complex number represented on the complex plane: (3,2) 2 + 3i 3 + 2i 3 � 2i 0 1 2 3 E F Y Z [ \ a b u v w x y z � � � � � � � � � � � � � �����������Ÿ����������������qd���� j� h &� h &� EH��Uj�@yP � L � : : : : : : : . Answer: d Explaination: Reason: Total cards = 18 Complex Numbers MCQs Practice Sheet 1. 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 … ��ࡱ� > �� ���� �������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� '` �� � You can skip questions if … Choose your answers to the questions and click 'Next' to see the next set of questions. questions first and the harder questions last within each group of multiple-choice questions and again within each group of student-produced response questions. � : : : : : 9. Convert into rectangular form a. Convert into polar form (cis form) a. More.. : : : : � � � d � � � � � � � � � � � � � ���� Complex Numbers Quiz 2 1. Cards bearing numbers 3 to 20 are placed in a bag and mixed thoroughly. Please note that, as on the actual test form, approximately one third of the multiple-choice questions in this test guide are more complex questions that require 2–3 minutes . Some Get Chapter Wise MCQ Questions for Class 11 Maths with Answers PDF Free Download prepared here according to the latest CBSE syllabus and NCERT curriculum. They include both multiple-choice and student-produced response questions. Download latest questions with answers for Mathematics Complex Numbers in pdf free or … शिक्षण प्रक्रिया में शिक्षक को अनेक कार्य एक साथ करने पड़ते हैं जैसे लिखना, प्रश्न पूछना, स्पष्ट करना, प्रदर्शन करना आदि... शिक्षण कौशल ( Teaching Skill) 2. 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. But first equality of complex numbers must be defined. 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. $ J/ h �1 z 9. Don’t let the question position or question type deter you from answering questions. This is termed the algebra of complex numbers. Engineering Maths Multiple Choice questions Answers can help in interview preparation. EMBED Equation.3 a. EMBED Equation.3 b. EMBED Equation.3 c. EMBED Equation.3 d. EMBED Equation.3 6. Download JEE Mathematics Complex Numbers MCQs Set A in pdf, Complex Numbers chapter wise Multiple Choice Questions free. Having introduced a complex number, the ways in which they can be combined, i.e. Tags: ... How to Effectively Answer CBSE Board Examination Question Papers. The complex number 2 + 4i is one of the root to the quadratic equation x 2 + bx + c = 0, where b and c are real numbers. . We have provided Complex Numbers and Quadratic Equations Class 11 Maths MCQs Questions with Answers to help students understand the concept very well. A complex number is of the form i 2 =-1. If you searching to check on Complex Numbers Multiple Choice Pdf And Income Tax Multiple Choice Questions And Answers Pdf price. 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) …………. 9. Perform the operations and write the result in standard form. Register for online coaching for IIT JEE (Mains & Advanced), NEET, Engineering and Medical entrance exams. Then(a) a² = b(b) a² = 2b(c) a² = 3b(d) a² = 4b, Answer: (c) a² = 3bHint:Given, z1 and z2 be two roots of the equation z² + az + b = 0Now, z1 + z2 = -a and z1 × z2 = bSince z1 and z2 and z3 from an equilateral triangle.⇒ z12 + z22 + z32 = z1 × z2 + z2 × z3 + z1 × z3⇒ z12+ z22 = z1 × z2 {since z3 = 0}⇒ (z1 + z2)² – 2z1 × z2 = z1 × z2⇒ (z1 + z2)² = 2z1 × z2 + z1 × z2⇒ (z1 + z2)² = 3z1 × z2⇒ (-a)² = 3b⇒ a² = 3b, Question 10:The complex numbers sin x + i cos 2x are conjugate to each other for(a) x = nπ(b) x = 0(c) x = (n + 1/2) π(d) no value of x, Answer: (d) no value of xHint:Given complex number = sin x + i cos 2xConjugate of this number = sin x – i cos 2xNow, sin x + i cos 2x = sin x – i cos 2x⇒ sin x = cos x and sin 2x = cos 2x {comparing real and imaginary part}⇒ tan x = 1 and tan 2x = 1Now both of them are not possible for the same value of x.So, there exist no value of x, Question 11.The curve represented by Im(z²) = k, where k is a non-zero real number, is(a) a pair of striaght line(b) an ellipse(c) a parabola(d) a hyperbola. 9+40i 11. Free PDF download of RD Sharma Solutions for Class 11 Maths Chapter 13 - Complex Numbers solved by Expert Mathematics Teachers on Vedantu.com. If points corresponding to the complex numbers z 1, z 2 and z 3 in the Argand plane are A,B and C respectively and if D ABC is isosceles, and right angled at B then a possible value of is (a) 1 (b) 1 (c) i (d) None of these. Answer/ Explanation. शिक्षण कौशल (Teaching Skill) 9i(3i) 27i -27i 27 -27 7. EMBED Equation.3 45 27 9 + 36i -27 - 36i 5. .? 10. h &� CJ UVaJ j� h &� h &� EH��Uj�@yP The section contains questions on deMoivre’s theorem, trigonometric functions expansion, complex conjugates, complex plane regions, complex numbers logarithm, powers and roots. � �� �� �� � � � � � � � � � $ � �. Multiple choice questions on number system quiz answers PDF covers MCQ questions on topics: Properties of real numbers, rational numbers, irrational numbers, complex numbers, basic function, binary operation, De Moivre’s theorem, groups, linear and quadratic function, sets, operation on three sets, and relation. All Chapter-13 Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. 1) True or false? . &. Choose the one alternative that best completes the statement or answers the question. A complex number is usually denoted by the letter ‘z’. . ‘a’ is called the real part, and ‘b’ is called the imaginary part of the complex number. Absolute Value, Complex Numbers. 8 cis 45 Check the below NCERT MCQ Questions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations with Answers Pdf free download. The probability that the number on the card taken out is an even number, is. 3 – 2i. . A card is taken out from the bag at random. EMBED Equation.3 29 EMBED Equation.3 EMBED Equation.3 21 3. Y, � ,2 � � ,2 4 �- ,2 � �- 8 : : � : : : : : 9. 5 cis 36.87 b. Probability Questions And Answers Pdf Question 11. Engineering Maths Objective type Questions Answers are also used at SSC and HSc level for Exam preparation. ... Free JEE Mathematics Complex Numbers Online Mock Test with important multiple choice questions as per JEE syllabus. 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. शिक्षण प्रक्रिया में शिक्षक को अनेक कार्य एक साथ करने पड़ते हैं जैसे लिखना, प्रश्न पूछना, स्पष्ट करना, प्रदर्शन करना... MCQ Questions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic... 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Get the most authentic answers for your subjective questions 31. Complex Numbers Chapter Exam Instructions. Multiple choice questions on number system quiz answers PDF covers MCQ questions on topics: Properties of real numbers, rational numbers, irrational numbers, complex numbers, basic function, binary operation, De Moivre’s theorem, groups, linear and quadratic function, sets, operation on three sets, and relation. 3+4i b. EMBED Equation.3 8i -8i 6i -6i 9. 3-√-2 a. 2+2i b. All quizzes are paired with a … MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. 2 - 2i c. -2i d. 2i 2. (3i)(2i) 6i -6i 6 -6 8. addition, multiplication, division etc., need to be defined. C ell references but not values d. Value and cell references Q. To create a formula, you can use: a. � : : : �. 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