{"id":1222,"date":"2021-12-17T17:57:58","date_gmt":"2021-12-17T12:27:58","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=1222"},"modified":"2024-01-17T15:53:07","modified_gmt":"2024-01-17T10:23:07","slug":"ncert-solutions-for-class-11-maths-chapter-5-complex-numbers-and-quadratic-equations","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/maths\/chapter-5-complex-numbers-and-quadratic-equations\/","title":{"rendered":"NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations"},"content":{"rendered":"

Subject specialists have created NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations, which includes thorough solutions for reference. All of the questions from the textbook’s exercises are answered here. Students can use these answers to help them prepare for their exams. The NCERT Solutions for Class 11<\/a><\/span><\/strong> provide useful solutions for improving conceptual knowledge.<\/span> <\/span><\/p>\n

The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Solutions for Class 11. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 11 pupils perform well in upcoming competitive exams.<\/span> <\/span><\/p>\n

The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.<\/span> <\/span><\/p>\n

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations<\/span><\/b> <\/span><\/p>\n\n\n\n\n\n\n
Exercise 5.1 Solutions<\/a><\/span><\/td>\n<\/tr>\n
Exercise 5.2 Solutions<\/a><\/span><\/td>\n<\/tr>\n
Exercise 5.3 Solutions<\/a><\/span><\/td>\n<\/tr>\n
Miscellaneous Exercise Solutions<\/a><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

NCERT Solutions for Class 11 Maths Chapter 5- Complex Numbers and Quadratic Equations<\/span><\/b> <\/span><\/p>\n

Three exercises and a miscellaneous exercise are included in Chapter 5 of Class 11 Complex Numbers and Quadratic Equations to assist students in practicing the required amount of problems in order to grasp all concepts. This chapter’s PDF of NCERT Solutions for Class 11 discusses the following themes and sub-topics:<\/span> <\/span><\/p>\n

5.1 Introduction<\/span><\/b> <\/span><\/p>\n

Some quadratic equations, we know, have no true solutions. That is, complex numbers are used in the solution of such equations. We’ve discovered the solution to the quadratic equation <\/span><\/p>\n

ax2+bx+c=0,ax2+bx+c=0,<\/span><\/p>\n

where <\/span><\/p>\n

D=b2\u22124ac<0D=b2\u22124ac<0<\/span><\/p>\n

5.2 Complex Numbers<\/span><\/b> <\/span><\/p>\n

This section covers the definition of complex numbers, as well as examples and explanations of the real and imaginary sections of complex numbers. NCERT Supplementary Exercise Solutions PDF for Class 11 Maths<\/a><\/span><\/strong> assists students in fully comprehending the questions.<\/span> <\/span><\/p>\n

5.3 Algebra of Complex Numbers<\/span><\/b> <\/span><\/p>\n

5.3.1 Addition of two complex numbers<\/span> <\/span><\/p>\n

5.3.2 Difference of two complex numbers<\/span> <\/span><\/p>\n

5.3.3 Multiplication of two complex numbers<\/span> <\/span><\/p>\n

5.3.4 Division of two complex number<\/span> <\/span><\/p>\n

5.3.5 Power of i<\/span> <\/span><\/p>\n

5.3.6 The square roots of a negative real number<\/span> <\/span><\/p>\n

5.3.7 Identities <\/span> <\/span><\/p>\n

Students will be able to comprehend the basic BODMAS operations on complex numbers, as well as their properties, power of I square root of a negative real number, and identities of complex numbers, after completing this exercise.<\/span> <\/span><\/p>\n

5.4 The Modulus and the Conjugate of a Complex Number<\/span><\/b> <\/span><\/p>\n

From this section, students learn about the modulus and conjugate of a complex number with the help of solved examples.<\/span> <\/span><\/p>\n

5.5 Argand Plane and Polar Representation<\/span><\/b> <\/span><\/p>\n

5.5.1 A complex number’s polar representation How to write ordered pairs for given complex numbers, the definition of a Complex plane or Argand plane, and the polar representation of ordered pairs in terms of complex numbers have all been covered in this part.<\/span> <\/span><\/p>\n

    \n
  1. A number of the form a + ib, where a and b are real numbers, is called a complex number, \u201c<\/span>a\u201d<\/span><\/i> is called the real part and \u201c<\/span>b\u201d<\/span><\/i> is called the imaginary part of the complex number<\/span> <\/span><\/li>\n<\/ol>\n

    Let <\/span><\/p>\n

    z1=a+ib <\/span><\/p>\n

    and <\/span><\/p>\n

    z2=c+id <\/span><\/p>\n

    Then<\/span> <\/span><\/p>\n

    z1+z2=(a+c)+i(b+d) <\/span><\/p>\n

    z1z2=(ac\u2212bd)+i(ad+bc) <\/span><\/p>\n

    For any non-zero complex number z = a + ib (a \u2260 0, b \u2260 0), there exists a complex number, denoted by 1\/z or z\u20131, called the multiplicative inverse of z<\/span> <\/span><\/p>\n

    For any integer <\/span><\/p>\n

    k,i4k+1=i,i4k+2=\u22121,i4k+3=\u2212ik,i4k+1=i,i4k+2=\u22121,i4k+3=\u2212i<\/span><\/p>\n

    The polar form of the complex number z = x + iy is r (cos\u03b8 + i sin\u03b8)<\/span> <\/span><\/p>\n

    A polynomial equation of n degree has n roots.<\/span> <\/span><\/p>\n

    Frequently Asked Questions on NCERT Solutions for Class 11 Maths Chapter 5 <\/strong><\/p>\n

      \n
    1. What are the topics covered under each exercise of NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations? <\/span><\/li>\n
    2. Explain the marks distribution in NCERT Solutions for Class 11 Maths? <\/span><\/li>\n
    3. Does Infinity Learn give the most reliable answers in Chapter 5 of NCERT Solutions for Class 11 Maths?<\/span><\/li>\n<\/ol>\n

      1. What are the topics covered under each exercise of NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations? <\/strong><\/p>\n

      The NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations include exercise-by-exercise problems that cover quadratic equations and complex numbers equations. These solutions give students a better understanding of complex number ideas and theorems. There are three exercises in this chapter, and the solutions are available in PDF format here. The first task is about finding the multiplicative inverse, the second is about finding the modulus and argument of a collection of numbers, and the third is about solving quadratic equations.<\/span> <\/span><\/p>\n

      2. Explain the marks distribution in NCERT Solutions for Class 11 Maths? <\/strong><\/p>\n

      The marks are given in about 6 units in the NCERT Solutions for Class 11 Maths.<\/span> <\/span><\/p>\n

        \n
      • Sets and Functions is the first unit (60 marks)<\/span> <\/span><\/li>\n
      • Algebra is the second unit (30 marks)<\/span> <\/span><\/li>\n
      • Coordinate Geometry is the third unit (10 marks)<\/span> <\/span><\/li>\n
      • Calculus is the fourth unit (30 marks)<\/span> <\/span><\/li>\n
      • Mathematical Reasoning and Statistics is the fifth unit (10 marks)<\/span> <\/span><\/li>\n
      • Probability is the sixth unit (30 marks)<\/span> <\/span><\/li>\n<\/ul>\n

        3. Does Infinity Learn give the most reliable answers in Chapter 5 of NCERT Solutions for Class 11 Maths? <\/strong><\/p>\n

        Infinity Learn has the most exact and dependable NCERT Solutions for Class 11 Maths Chapter 5. Students can quickly download the solutions, which are available in PDF format, and use them to prepare for the term – I test. The solutions are framed and prepared by a group of experienced academics with years of experience in the various areas. The most in-depth solutions to the exercise-by-exercise challenges have been compiled with the goal of assisting students in acing the first-term exam without anxiety.<\/span> <\/span><\/p>\n

        <\/span><\/p>\n

        <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

        Subject specialists have created NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations, which includes thorough […]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"NCERT Solutions for Class 11 Maths Chapter 5","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Download Free PDF of NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations solved by Expert Teachers as per NCERT (CBSE) textbook guidelines. All Chapter 5 Complex Numbers and Quadratic Equations Exercises Questions with Solutions to help you to revise the complete Syllabus and boost your score in examinations.","custom_permalink":"study-materials\/ncert-solutions\/class-11\/maths\/chapter-5-complex-numbers-and-quadratic-equations\/"},"categories":[19,25],"tags":[],"table_tags":[],"acf":[],"yoast_head":"\nNCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Download Free PDF of NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations solved by Expert Teachers as per NCERT (CBSE) textbook guidelines. 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