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JEE Main - Complex Numbers and Quadratic Equations Notes (Free PDF Download)

Last updated date: 06th Dec 2023
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MVSAT Dec 2023

Download JEE Main Complex Numbers and Quadratic Equations Notes with Important Topics and Prepare Efficiently

Prepare effectively for JEE Main by downloading the Complex Numbers and Quadratic Equations Notes with important topics. These notes, Prepared by our master teachers, simplify complex concepts, highlight key points, and provide important topics. You can download them for free from our website. These comprehensive revision notes condense the essential information you need to know, making your preparation efficient. As you delve into the topics covered, you'll enhance your understanding and be well-prepared for the exam. Get ready to excel in JEE Main with these valuable resources at your disposal.


JEE Main Revision Notes


Text, Images, Videos and PDF


JEE Main

Chapter Name:

Complex Numbers and Quadratic Equations

Academic Session:



English Medium



Available Material:

Chapter-wise Notes with PDF

In the chapter ‘Complex Numbers and Quadratic Equations,’ important concepts include:

  • Complex Numbers: Understanding imaginary unit $\bar{i}$, real and imaginary parts, complex conjugates, and operations (addition, multiplication).
  • Quadratic Equations: Solving using factorization, completing the square, quadratic formula; nature of roots, discriminant; relationships between coefficients and roots.

These are some of the key topics for the JEE Main exams. Looking at the old JEE Main question papers, you'll see the total weightage of questions from this chapter is 7%. Take a look at the table for more details.

Year Wise Weightage of Questions: JEE Main Complex Numbers and Quadratic Equations

Sl. No.


Average No. Of Questions Asked

Marks per Question

Total Marks





















Over the last five years of JEE Main exams, about 3 questions were asked from Complex Numbers and Quadratic Equations. Now you know how much weightage you have to give to this chapter. The teachers put in dedicated efforts to ensure the Complex Numbers and Quadratic Equations notes align perfectly with the JEE Main syllabus. Get ready to do well – get your Complex Numbers and Quadratic Equations Notes and shine in JEE Main 2024!

Competitive Exams after 12th Science

JEE Main 2024: Must-ReviseTopics in Complex Numbers and Quadratic Equations

Let's focus on the key topics you should review in Complex Numbers and Quadratic Equations. These important topics can make a real difference in your preparation. Mastering them will give you a strong edge in the upcoming exam. Let's dive into the must-revise topics to help you shine in JEE Main 2024.

Complex Numbers:

  • Definition of Complex Numbers

  • Complex Plane (Argand Diagram)

  • Polar Form and Euler's Formula

  • Operations with Complex Numbers (Addition, Subtraction, Multiplication, Division)

  • Conjugate of a Complex Number

  • Modulus (Magnitude) and Argument of a Complex Number

  • De Moivre's Theorem

  • Roots of Complex Numbers

  • Complex Conjugate Roots Theorem

  • Complex Exponential Form

Quadratic Equations:

  • Solving Quadratic Equations by Factoring

  • Quadratic Formula

  • Completing the Square Method

  • Discriminant and Nature of Roots

  • Sum and Product of Roots

  • Quadratic Equations in Real-Life Applications

  • Quadratic Inequalities

  • Graphs of Quadratic Equations

  • Relationship between Roots and Coefficients

  • Vieta's Formulas

Maths Notes for JEE Main 2024 Chapters: Links Available

Make your JEE Main Maths studying for 2024 even better using our notes organized by chapter. FindThe links in the table below for easy access.

The Significance of Complex Numbers and Quadratic Equations Notes for JEE Main 2024

Unravel the enigmatic realm of Complex Numbers and Quadratic Equations – a chapter that unveils the captivating interplay between real and imaginary numbers. Get ready to embark on an interactive journey that will not only enhance your mathematical prowess but also leave you mesmerized by the magic of numbers.

Complex Numbers: The Gateway to Imagination

Imagine numbers that defy the boundaries of reality – welcome to the world of complex numbers! With real numbers as companions, complex numbers bring a touch of imagination to mathematics. Expressions like $\sqrt{-1}$ become a reality, giving birth to the enigmatic 'imaginary unit,' denoted as 'i.' With this intriguing building block, you'll explore the complex plane, where numbers reside like stars in the mathematical cosmos.

Key Highlights:

  • Imaginary Unit 'i': Discover the wonders of 'i' and its remarkable power to bring the impossible to life.

  • Complex Plane Exploration: Navigate the complex plane like an explorer charting new territories.

  • Real and Imaginary Components: Witness the synergy of real and imaginary components that form the essence of complex numbers.

Quadratic Equations: Unraveling Mysteries of Second Degree 

Step into the realm of quadratic equations – a world where x², coefficients, and solutions dance in perfect harmony. This chapter demystifies the quadratic equation ax² + bx + c = 0, where you'll decode its secrets, discover its solutions, and even learn how to unveil its hidden roots!

Key Highlights:

  • Roots and Solutions: Dive deep into the process of finding roots and solutions of quadratic equations.

  • Nature of Roots: Uncover the intriguing possibilities of real and complex roots based on the discriminant.

  • Quadratic Formula: Learn the magical quadratic formula that unveils solutions with mathematical elegance.

Interactive Engagements Await! 

  • Mathematical Riddles: Challenge yourself with brain-teasing riddles that involve complex numbers and quadratic equations. Unleash your problem-solving skills!

  • Visual Explorations: Immerse yourself in interactive visualizations that bring complex numbers and quadratic equations to life, making learning an unforgettable experience.

  • Real-World Connections: Discover how these mathematical concepts transcend the classroom and find applications in diverse fields like physics, engineering, and even arts.

Elevate your JEE Main 2024 Journey! 

Complex Numbers and Quadratic Equations are more than formulas – they're gateways to new dimensions of mathematical understanding. Equip yourself with the tools to solve problems, unravel mysteries, and embrace the magic of numbers. Let this chapter be your compass, guiding you towards mathematical excellence and sparking your curiosity along the way. Get ready to embark on a mathematical adventure that's both captivating and rewarding!

D: Formulaic Support: Boosting Understanding with Revision Note Integration

If you want to learn well, you can use a clever plan by merging formulas and revision notes. Formulas are like short explanations of important concepts. You get a complete learning method when you use them with detailed revision notes. Revision notes build a strong foundation, and formulas help you grasp concepts and solve problems.This combination makes tough things simpler and improves memory. Following this approach can enhance your understanding and help you perform well in your studies.

Download Vedantu's JEE Main Maths Formulas for FREE. Blend it with JEE Main Notes, and you'll notice positive score changes.

E: Next Steps: Further Resources for JEE Main 2024 Complex Numbers and Quadratic Equations

Ready to take your JEE Main 2024 Complex Numbers and Quadratic Equations preparation up a notch? Delve into these crucial resources:

  • Practice Papers: Hone your skills with targeted practice.

  • Mock Tests: Simulate exam conditions and boost your confidence.

  • Sample Papers: Familiarize yourself with the question patterns.

  • Previous Year Question Papers (PYQPs): Gain insights into the exam's structure and trends.

Combine these resources to refine your understanding and exam-taking abilities. Elevate your performance for JEE Main 2024!

Here are the links for the additional resources of JEE Main 2024:

F: Get Ahead in your Exams with Vedantu’s JEE Main Notes

In your journey towards exam success, Vedantu's Complex Numbers and Quadratic Equations JEE Main Notes are your trusted companion. Our unique approach, combining expert guidance and student-friendly resources, sets us apart. With comprehensive revision notes at your fingertips, complex concepts become clear and preparation becomes more efficient. What's more, These valuable resources are available to you as FREE PDFs. Trust Vedantu to help you stride confidently towards acing your exams. Elevate your learning experience, simplify your studies, and embrace excellence with Vedantu.

FAQs on JEE Main - Complex Numbers and Quadratic Equations Notes (Free PDF Download)

1. What are the most important topics included in Complex Numbers and Quadratic Equations Notes for JEE Main 2024?

The following crucial subjects are covered in the Complex Numbers and Quadratic Equations Notes for JEE Main 2024:

Complex Numbers:

  • Representation of complex numbers in the form $\bar{a+bi}$, where $\bar{a}$ and $\bar{b}$ are real numbers and $\bar{i}$ is the imaginary unit.

  • Arithmetic operations with complex numbers: addition, subtraction, multiplication, and division.

  • Modulus and argument of complex numbers.

  • Polar form of complex numbers and conversion between rectangular and polar forms.

  • De Moivre's theorem and its applications.

  • Roots of complex numbers, including the concept of nth roots.

  • Geometrical representation of complex numbers in the complex plane.

  • Complex conjugates and properties.

Quadratic Equations:

  • Solving quadratic equations using factorization.

  • Finding roots of quadratic equations using the quadratic formula.

  • Discriminant and its significance in determining the nature of roots.

  • Nature of roots: real, imaginary, equal, or distinct.

  • Relation between coefficients and roots.

  • Sum and product of roots.

  • Quadratic equations with real coefficients and complex roots.

2. What is the weightage of Complex Numbers and Quadratic Equations Notes for JEE Main 2024?

The weightage of the Complex Numbers and Quadratic Equations chapter in JEE Main 2024 is around 7-8%. This means that there are typically 1-2 questions asked from this chapter.

3. Which is the easiest topic of JEE Main 2024 Complex Numbers and Quadratic Equations Notes?

The topic 'Complex Numbers' is often considered one of the easier sections in JEE Main 2024's syllabus for many students. It introduces the concept of imaginary and complex numbers, along with basic operations and properties. Familiarity with algebraic manipulation and an understanding the geometric representation can aid in mastering this topic efficiently.

4. How much time is required to prepared for JEE Main 2024 Complex Numbers and Quadratic Equations Notes?

The amount of time needed to prepare for JEE Main 2024 Complex Numbers and Quadratic Equations Notes depends on your familiarity with the concepts, study habits, and practise attempts. A few weeks of consistent study, involving active reading, problem-solving, and revision, should provide a solid foundation on average. However, it is critical to adjust your study schedule to your learning rate and set aside enough time for thorough comprehension and practise.

5. Where can I get other materials to supplement the JEE Main 2024 Complex Numbers and Quadratic Equations Notes?

Vedantu's website contains additional materials to help you prepare for JEE Main 2024 Complex Numbers and Quadratic Equations. These tools provide practise papers, video lectures, interactive quizzes, and conversations to supplement your JEE Main materials, improving your comprehension and exam readiness.

6. How can I make my own JEE Main Complex Numbers and Quadratic Equations notes?

Here are some tips on how to make your own JEE Main Complex Numbers and Quadratic Equations notes:

  • Start by reading your textbook or a good online resource on Complex Numbers and Quadratic Equations.

  • Take notes on the important concepts and formulas.

  • Organize your notes in a way that makes sense to you.

  • Add diagrams and illustrations to help you understand the concepts.

  • Practice solving problems from your notes

7. What is Complex Numbers and Quadratic Equations in the context of JEE Main 2024?

In the context of JEE Main (Joint Entrance Examination Main), complex numbers refer to numbers with both real and imaginary components. Quadratic equations involve second-degree polynomial equations, often leading to solutions that can be real or complex. Both topics are crucial in mathematics and are tested in the JEE Main exam to assess candidates' understanding of algebraic concepts.

8. Are there any common mistakes students make in Complex Numbers and Quadratic Equations problems?

Common mistakes students make in Complex Numbers and Quadratic Equations problems include:

  • Forgetting the imaginary unit 'i' in complex numbers.

  • Mishandling square roots when simplifying expressions.

  • Incorrectly applying the quadratic formula or making sign errors.

  • Ignoring the possibility of multiple solutions.

  • Misinterpreting the meaning of roots in context.