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

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations describe the properties of complex numbers and their use in finding the roots of quadratic equations. Students are familiar with finding the roots of a quadratic equation in the real numbers set with a non-negative discriminant. In this chapter, they will learn how to solve a quadratic equation with a negative discriminant value. The knowledge of Complex Numbers and Quadratic Equations is particularly useful in advanced calculus. These equations are widely applied in solving algebraic problems. The geometric graph of these equations represents a parabola that doesn’t intersect the x-axis on a quadratic plane. NCERT Solutions Class 11 Maths Chapter 5 will offer the right foundational skills required by students to study these equations and their applications.

Gaining a gradual understanding of complex numbers and operations performed on them is vital for understanding complex roots. The well-explained step-by-step illustrative format of these solutions helps to implement a thorough practice of all topics. Several concepts, formulas, theorems, and problems are explained in these solutions to provide a clear understanding of complex numbers and quadratic equations. With the regular revision of Class 11 Maths NCERT Solutions Chapter 5, students will quickly master how to solve these equations. To learn and practice with NCERT Solutions Chapter 5 Complex Numbers and Quadratic Equations, download the exercise-wise solutions provided in the links below.

• NCERT Solutions Class 11 Maths Chapter 5 Ex 5.1
• NCERT Solutions Class 11 Maths Chapter 5 Ex 5.2
• NCERT Solutions Class 11 Maths Chapter 5 Ex 5.3
• NCERT Solutions Class 11 Maths Chapter 5 Miscellaneous Ex

NCERT Solutions for Class 11 Maths Chapter 5 PDF

NCERT Solutions for Class 11 Maths Chapter 5 is geared towards easy and proficient math learning. The self-explanatory composition of exercises, examples, and illustrations present in these solutions are highly reliable to study the complete syllabus of this chapter. These resources are a highly reliable means of gaining clear and extensive knowledge of complex numbers and their use in algebra. To learn and practice Complex Numbers and Quadratic Equations with these solutions, click on the pdf file links given below.

☛ Download Class 11 Maths NCERT Solutions Chapter 5

NCERT Class 11 Maths Chapter 5  Download PDF

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

NCERT solutions Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations are advantageous for promoting students’ fundamental algebraic skills. These well-researched resources offer systematic learning of complex concepts and topics related to them. The considerate blend of illustrations and sample questions incorporated in these solutions is adequate to form the core basics required for solving quadratic equations. With the practice of these solutions, it becomes quite convenient to prepare and revise for exams. To practice the exercise-wise NCERT Solutions Class 11 Maths Complex Numbers and Quadratic Equations, try the links given below.

• Class 11 Maths Chapter 5 Ex 5.1 - 14 Questions
• Class 11 Maths Chapter 5 Ex 5.2 - 8 Questions
• Class 11 Maths Chapter 5 Ex 5.3 - 9 Questions
• Class 11 Maths Chapter 5 Miscellaneous Ex - 20 Questions

☛ Download Class 11 Maths Chapter 5 NCERT Book

Topics Covered: The important topics included in NCERT solutions Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations are an introduction to complex numbers, algebra of complex numbers, modulus, and conjugate of a complex number. These solutions comprise important formulas and theorems based on the subtopics like the addition of complex numbers, difference of complex numbers, multiplication of complex numbers, division of two complex numbers, power of i, and square roots of a negative real number identities.

Total Questions: Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations has 31 questions in 3 exercises plus 20 questions in a miscellaneous exercise. These questions are majorly aligned towards imparting a deep understanding of complex numbers, quadratic equations, their applications, theorems, and formulas.

List of Formulas in NCERT Solutions Class 11 Maths Chapter 5

Formulas are an indispensable part of algebra, and therefore, it is vital to memorize formulas for scoring better in exams. Learning formulas, important terms, and concepts related to Complex Numbers and Quadratic Equations will also enable students to form a firm foundation required for mastering these topics. NCERT Solutions Class 11 Maths Chapter 5 is a valuable aid in gaining a detailed knowledge of all the formulas and concepts. These are well-explained for students to imbibe them better. Some of the important terms, formulas, and concepts related to Complex Numbers and Quadratic Equations explained in these solutions are listed below:

• Complex Numbers: Complex Numbers are the numbers of the form a + ib, where a and b are real numbers.

• Addition of Complex Numbers (a+bi) + (c+di) = (a+c) + (b+d)i

• Subtraction of Complex Numbers (a+bi) − (c+di) = (a−c) + (b−d)i

• Multiplication of Complex Numbers (a+bi) × (c+di) = (ac−bd) + (ad+bc)i

• Multiplication Conjugates (a+bi)(a+bi) = a² + b²

• Division of Complex Numbers

(a+bi)/(c+di) = (a+bi/c+di) × (c−di) / (c−di) = (ac+bd / c²+d²) + (bc−ad / c²+d²)i

• Equality of Complex Numbers Formula

a+bi = c+di ⇔ a = c and b = d

• Fundamental theorem of Algebra: The fundamental theorem of algebra states that every polynomial equation having complex coefficients and degree >=1 has at least one complex root. This theorem also holds true for the equations with real coefficients, as real numbers are also complex numbers with an imaginary part.

• Roots of Quadratic Equation: The roots of a quadratic equation ax² + bx + c = 0 are given by the formula:

x = [-b±√(b²-4ac)]/2a