Complex Numbers & Quadratic Equations JEE Mains Previous Year Questions with Solutions and Weightage

Complex numbers and Quadratic equations are important and high-weightage topics that are asked both in the JEE Main and JEE Advanced Exam. The topics carry an approximate weightage of 7-9% and candidates can expect 2 to 3 questions from this section in the exam.

The complex number section focuses on understanding the imaginary numbers, modulus, and properties of complex roots, while the quadratic section focuses on properties and solutions of quadratic expressions.

The most asked topics in the Complex numbers and quadratic equations are Argand Plane, Roots of Unity, Nature of Roots, and Complex conjugates.

Must Read Articles:

• Download JEE Main Last 10-year PYQ for Free
• Download JEE Main 2025 Shift 1 Question Paper with Detailed Solutions

Below is the list of Complex numbers and quadratic equations questions with detailed solutions asked in JEE Main.

Question 1:

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Question 2:

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Question 3:

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Question 4:

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Question 5:

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Question 6:

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Question 7:

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Question 8:

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Question 9:

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Question 10:

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JEE Main Mathematics Paper Pattern

The NTA has updated the JEE Main Mathematics Exam Pattern for 2025. Earlier, section B allowed candidates to attempt only 5 out of 10 NVQs, but now all 5 are compulsory.

The detailed exam pattern for JEE Main Mathematics is given below:

JEE Main Mathematics Chapter-Wise Weightage

Calculus and algebra are the most important sections in the JEE Main Mathematics. These topics carry approximately 35 to 40% weightage in the exam.

The detailed chapter-wise weightage for mathematics is given in the table below for classes 11th and 12th.

Class 11 Mathematics High-weightage Topics:

Mathematics Chapter-wise Weightage for Class 12 Topics:

JEE Main Last 5 Year Mathematics Papers Pdf

You can download the JEE Main last 5 years’ Mathematics pdf with solutions from the table given below:

JEE Main 2024 Mathematics Question Paper Session 1

JEE Main 2024 Mathematics Question Paper Session 2

JEE Main 2023 Mathematics Question Paper

JEE Main 2023 Mathematics Question Paper Session 1

JEE Main 2022 Mathematics Question Paper with Solution PDF

JEE Main 2022 Mathematics Question Paper with Solution PDF- Phase 1

JEE Main 2021 Mathematics Question Paper- Download PDF

JEE Main 2021 Mathematics Question Paper with Solution (Session 4- August)- Download PDF

JEE Main 2021 Mathematics Question Paper with Solution (Session3- July)- Download PDF

JEE Main 2021 Mathematics Question Paper with Solution (Session 2- March)- Download PDF

JEE Main 2021 Mathematics Question Paper with Solution (Session 1- February)- Download PDF

JEE Main 2020 Mathematics Question Paper with Solutions- Download PDF

JEE Main 2020 Mathematics Question Paper with Solutions (Session 2- September)- Download PDF

JEE Main 2020 Mathematics Question Paper with Solutions (Session 1- January)- Download PDF

Important Books for Mathematics:

• NCERT Mathematics Class 11th Books
• NCERT Mathematics Class 12th Books

Frequently Asked Questions

How are complex numbers related to quadratic equations?

Complex numbers play a major role in solving quadratic equations when the equation has no real roots. In a quadratic equation of the form ax2 +bx+c= 0, the nature of the root depends on the discriminant.

• If the discriminant is positive, the equation has two real roots.
• If the discriminant is zero, the equation has one repeated real root.
• If the discriminant is negative the equation has no real roots.

Why is 17 a complex number?

17 is considered as a real number, it can also be expressed as complex number. A complex number can be written in the form of a+bi, where a and b are real numbers, and i is the imaginary number.

In the case of 17, the value of b can be zero and it can be written as 17+ 0i. This shows that all real numbers are complex with their imaginary part equal to zero.

How many complex roots does a quadratic have?

A quadratic equation always has two roots. When the discriminant is negative, the equation has two complex roots that are conjugates of each other. For example, the quadratic equation x2 + 4=0 has a negative discriminant of -4. The roots of this equation will be x=2i and x= -2i which are complex conjugates.

What happens when a quadratic has complex zero?

When a quadratic equation has complex zeros, the graph of such an equation does not touch or cross the x-axis. The parabola lies above or below the x-axis.

For example, the graph of y=x2+4 stays above the x-axis because the minimum value of parabola is 4. The roots of this equation are ±2i which is imaginary and thus, has no real x-intercepts.

What is the imaginary unit I equal to?

The imaginary unit I is defined as the square root of -1. Written mathematically as: i= √−1

There is no real number that is squared and becomes equal to a negative value, so I represent a unique concept i.e. imaginary number. The rules of imaginary number i are as follows:

• i2=-1
• i3=-i
• i4= 1

These rules are important to solving quadratic equations having negative discriminants.