# 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.

**ā** Download Class 11 Maths NCERT Solutions Chapter 5

**NCERT Class 11 Maths Chapter 5 **

### 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

ā 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) = a^{2}+ b^{2}

**Division of Complex Numbers**

(a+bi)/(c+di) = (a+bi/c+di) × (c−di) / (c−di) = (ac+bd / c^{2}+d^{2}) + (bc−ad / c^{2}+d^{2})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±√(b^{2}-4ac)]/2a

## FAQs on NCERT Solutions Class 11 Maths Chapter 5

### What is the Importance of NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations?

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations are the most accurate and reliable means of math learning. These well-researched solutions written by math experts are highly prominent to encourage practice and confidence in students. The exercises provided in these solutions are apt to understand complex numbers concepts and their use in quadratic equations. With the regular practice of these solutions, it becomes pretty convenient to score well in exams.

### What are the Important Topics Covered in Class 11 Maths NCERT Solutions Chapter 5?

NCERT Solutions Class 11 Maths Chapter 5 starts with an introduction to complex numbers, algebra of complex numbers, and their polar representation. The subtopics covered under these topics are the sum of complex numbers, differences of complex numbers, product, division of complex numbers, power of i, square roots of a negative real number, modulus, and conjugate of complex numbers. The other important topics covered in this chapter are based on solving quadratic equations with complex roots and their fundamental theorems.

### Do I Need to Practice all Questions Provided in NCERT Solutions Class 11 Maths Complex Numbers and Quadratic Equations?

NCERT Solutions Class 11 Maths Complex Numbers and Quadratic Equations are well-curated for students to learn complex numbers with ease. Every question included in these solutions provides conceptual clarity for kids to master them easily. The fundamental knowledge of Complex Numbers and Quadratic Equations, as well as their use, will allow children to apply their knowledge to practical situations. These solutions also form the basis for studying advanced math topics, including calculus.

### How Many Questions are there in Class 11 Maths NCERT Solutions Chapter 5 Complex Numbers and Quadratic Equations?

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations has a total of 51 questions in 4 exercises. Solving and practicing these sums will help students gain a deep knowledge of important formulas, theorems, and arithmetic operations related to Complex Numbers and Quadratic Equations. The simplistic math vocabulary used in these solutions is quite proficient in easily imparting a clear and step-by-step understanding of each topic.

### What are the Important Formulas in NCERT Solutions Class 11 Maths Chapter 5?

NCERT Solutions Class 11 Maths Chapter 5 explains the formulas related to the sum and difference of two angles in Complex Numbers and Quadratic Equations. Some of the important concepts and formulas related to this topic are based on the arithmetic of complex numbers, fundamental theorem of algebra, and quadratic equations. These concepts are elaborated in detail with the help of engaging illustrations and examples.

### Why Should I Practice NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations?

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations is a comprehensive guide that promotes the accurate and precise knowledge of complex numbers and their use in quadratic equations. With the practice of these solutions, students can learn to excel in exams. Students can cover all the topics provided in the CBSE Class 11 Maths Chapter 5 by using these resources. The pattern of problems incorporated in these solutions is pretty amiable to deliver simple and easy learning.