Complex Numbers and Quadratic Equations Case Study Questions Class 11 Maths Chapter 4

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Last Updated on July 22, 2025 by XAM CONTENT

Hello students, we are providing case study questions for class 11 Maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 11 Maths. In this article, you will find case study questions for cbse class 11 Maths chapter 4 Complex Numbers and Quadratic Equations.

ChapterComplex Numbers and Quadratic Equations
Type of QuestionsCase Study Questions
Nature of QuestionsCompetency Based Questions
BoardCBSE
Class11
SubjectMaths
Useful forClass 11 Studying Students
Answers providedYes
Difficulty levelMentioned
Important LinkClass 11 Maths Chapterwise Case Study

Case Study Questions on Complex Numbers and Quadratic Equations

Case Study:
A physics lab models certain oscillations with the quadratic equation \( x^2 + 4x + 13 = 0 \), where \( x \) represents a variable related to the system’s state.

Additionally, the amplitude of oscillation (a real number) is connected to the modulus of the complex roots of the equation.

Questions:

  1. Find the roots of the quadratic equation \( x^2 + 4x + 13 = 0 \).
  2. Express the roots in the form \( a + ib \).
  3. Find the modulus of each root. What does it represent in this context?
  4. Briefly explain why complex roots arise in this physical model.

Solutions:

1. Roots of the quadratic equation:

\[ x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a} \] Here, \( a = 1, b = 4, c = 13 \): \[ x = \frac{-4 \pm \sqrt{16 – 52}}{2} = \frac{-4 \pm \sqrt{-36}}{2} = \frac{-4 \pm 6i}{2} \]

2. Roots in \( a + ib \) form:

\[ x = -2 + 3i,\quad x = -2 – 3i \]

3. Modulus of each root and its meaning:

\[ |x| = \sqrt{(-2)^2 + (3)^2} = \sqrt{4 + 9} = \sqrt{13} \]

The modulus \( \sqrt{13} \) represents the amplitude of oscillation in this system.

4. Explanation:
Complex roots arise here because the system modeled by the quadratic equation is underdamped (discriminant \( b^2 – 4ac < 0 \)), causing oscillatory motion. The real part indicates decay/growth, and the imaginary part relates to oscillation frequency, which is common in physics and engineering models.

We hope the given case study questions for Complex Numbers and Quadratic Equations Class 11 helps you in your learning.

Also check

Topics from which case study questions may be asked

  • Complex Numbers – Introduction and Definitions
  • Algebra of Complex Numbers
  • Modulus and Conjugate of a Complex Number
  • Argand Plane and Polar Representation
  • Quadratic Equations and Their Solutions
  • Nature of Roots and Discriminant
  • Solution of Quadratic Equations in Complex Numbers
  • Fundamental Theorem of Algebra (Statement Only)

Frequently Asked Questions (FAQs) on Complex Numbers and Quadratic Equations Case Study Questions

Q1: What is a case study question in mathematics?

A1: A case study question in mathematics is a problem or set of problems based on a real-life scenario or application. It requires students to apply their understanding of mathematical concepts to analyze, interpret, and solve the given situation.

Q2: How should students tackle case study questions in exams?

A2: To tackle case study questions effectively, students should:
Read the problem carefully: Understand the scenario and identify the mathematical concepts involved.
Break down the problem: Divide the case study into smaller parts to manage the information better.
Apply relevant formulas and theorems: Use the appropriate mathematical tools to solve each part of the problem.

Q3: Why are case study questions included in the Class 11 Maths curriculum?

A3: Case study questions are included to bridge the gap between theoretical knowledge and practical application. They help students see the relevance of what they are learning and prepare them for real-life situations where they may need to use these mathematical concepts.

Q4: Are there any online resources or tools available for practicing “Complex Numbers and Quadratic Equations” case study questions?

A12: We provide case study questions for CBSE Class 11 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.

Complex Numbers and Quadratic Equations Case Study Questions Class 11 Maths Chapter 4

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