Complex numbers class 11 miscellaneous exercise

r 2 = r = Now, cosθ = and sinθ = = cosθ = and sinθ = Therefore, θ = [As θ lies in the II quadrant] Question 14. Find the real numbers x and y if ( x – iy ) (3 + 5 i ) is the conjugate of – 6 – 24 i . Solution: Let us assume z = ( x– iy) (3 + 5 i) z = 3x + xi – 3yi – 5yi 2 = 3x + 5xi – 3yi + 5y = (3x + 5y) + i(5x – 3y) Question 18. Find the number of non-zero integral solutions of the equation |1 – i| x = 2 x Solution: |1 – i| x = 2 t x = 2x 2x – x = 0 Thus, ‘0’ is the only integral solution of the given equation. Therefore, the number of non-zero integral solutions of the given equation is 0. Question 19. If (a+ib) (c+id) (e+if) (g+ih) = A +iB, then show that (a 2+b 2) (c 2+d 2) (e 2+f 2) (g 2+h 2) = A 2+ B 2. Solution: Given: (a + ib)(c + id)(e + if)(g + ih) = A + iB Therefore, |(a + ib)(c + id)(e + if)(g + ih)| = |A + iB| = |(a + ib)| ×|(c + id)| ×|(e + if)| ×|(g + ih)| = |A + iB| On squaring both sides, we get ( a 2+ b 2) ( c 2+ d 2) ( e 2+ f 2) ( g 2+ h 2) = A 2+ B 2 Hence, proved. Question 20. If, then find the least positive integral value ofm. Solution: i m = 1 Hence, m = 4k, where k is some integer. Hence, the least positive integer is 1. Thus, the least positive integral value of mis 4 (= 4 × 1).

Tiwari Academy / NCERT Solutions / NCERT Solutions for Class 11 / NCERT Solutions for Class 11 Maths / NCERT Solutions for Class 11 Maths Chapter 4 Complex Numbers and Quadratic Equations / NCERT Solutions Class 11 Maths Chapter 4 Miscellaneous Exercise NCERT Solutions Class 11 Maths Chapter 4 Miscellaneous Exercise

NCERT Solutions for Class 11 Maths provides solutions that are easy to understand. The Solutions provided by GeeksforGeeks can help you to build a deeper understanding of the concepts like Sets, Relations & Functions, Complex numbers, Conic sections, etc. Our NCERT Class 11 Maths provide a step-by-step and extensive explanation of all the problems covered in the NCERT textbook. They serve as a guide for students who wish to double-check their answers to problems and for children who desire a better comprehension of subjects. These NCERT Solutions for Class 11are compiled and curated by certified Maths professionals who guarantee that students will build a strong foundation in Maths. Chapter 1– Sets Chapter 9– Sequences and Series Chapter 2– Relations and Functions Chapter 10– Straight Lines Chapter 3– Trigonometric Functions Chapter 11– Conic Sections Chapter 4– Principle of Mathematical Induction Chapter 12– Introduction to Three-dimensional Geometry Chapter 5– Complex Numbers and Quadratic Chapter 13– Limits and Derivatives Chapter 6– Linear Inequalities Chapter 14– Mathematical Reasoning Chapter 7– Permutations and Combinations Chapter 15– Statistics Chapter 8– Binomial Theorem Chapter 16– Probability NCERT Solutions for Class 11 Maths Chapter 1- Sets The Chapter covers Class 11 Maths NCERT Solutions Chapter 1- Sets which explains the concept of sets along with their representation. The topics discussed are empty sets, equal sets, subsets, finite and infinite sets, powe...

Complex Numbers Class 11 Complex Numbers Class 11 notes are provided here in detail. The concepts covered in complex numbers class 11 Maths are important for students, as it will help them to solve the problems in the higher class. Go through the notes provided below and practice the problems as well to score good marks in the examination. Complex Numbers:Â A number that can be represented in form p + iq is defined as a complex number. Here, p and q are real numbers and \(\begin \). 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. Complex Numbers Class 11 Concepts The topics and subtopics covered in Complex numbers class 11 are: • Introduction • Complex Numbers • Algebra of Complex Numbers • Addition of two complex Numbers • Difference of two complex Numbers • Multiplication of two complex Numbers • Division of two complex Numbers • Power of i • The square root of a negative real number • Identities • The Modulus and the Conjugate of a Complex Numbers • Argand Plane and Polar Representation • Polar Representation of a Complex Numbers Complex Numbers Class 11 Notes The notes for class 11 gives a detailed knowledge of all the concepts involved in complex numbers. Some important concepts like the algebra of complex number, what is the principal argument, modulus and argument of complex numbers, and so on. To learn more, click here: Consider two complex numbers...

NCERT Solutions Class 11 Maths Chapter 5 Miscellaneous Exercise Complex Numbers and Quadratic Equations NCERT Solutions for Class 11 Maths Chapter 5 Miscellaneous Exercise is an additional exercise to solidify the basic understanding of ☛ Download NCERT Solutions Class 11 Maths Chapter 5 Miscellaneous Exercise Miscellaneous Exercise Class 11 Chapter 5 Download PDF