Top Strategies to Score High in JEE Main 2025-26 Mock Tests on Complex Numbers and Quadratic Equations
Complex Numbers and Quadratic Equations is a fundamental chapter in JEE Main Maths, focusing on essential topics such as modulus, argument, quadratic roots, and properties of complex numbers. Practicing this mock test will reinforce your understanding and problem-solving skills, helping you confidently tackle similar JEE-level questions. Challenge yourself and strengthen your conceptual clarity with this expertly designed assessment!
Mock Test Instructions for the Complex Numbers And Quadratic Equations Mock Test-3:
- 20 questions from Complex Numbers And Quadratic Equations Mock Test-3
- Time limit: 20 minutes
- Single correct answer per question
- Correct answers appear in bold green after submission
How Can JEE Mock Tests Help You Master Complex Numbers and Quadratic Equations?
- Identify and overcome common mistakes in modulus, argument, and conjugate root problems.
- Accelerate conceptual learning by tackling quadratic roots and discriminant-based MCQs.
- Simulate real exam pressure with time-bound tests for chapter revision.
- Utilize detailed feedback to focus on weak areas within complex numbers and quadratic equations.
- Boost accuracy and speed for JEE Main Maths with consistent chapter-wise practice.
Excel in JEE Maths: Expert-Designed Mock Tests on Complex Numbers & Quadratic Equations
- Practice carefully curated questions reflecting the latest JEE Main exam pattern.
- Improve problem-solving agility with mixed-difficulty MCQs on all crucial subtopics.
- Master properties of complex numbers and quadratic equations through focused quizzes.
- Get instant answers and explanations to enhance self-assessment after each test.
- Refine formula application and error detection using expert-level question variety.
Subject-Wise Excellence: JEE Main Mock Test Links
| S.No. | Subject-Specific JEE Main Online Mock Tests |
|---|---|
| 1 | Online FREE Mock Test for JEE Main Chemistry |
| 2 | Online FREE Mock Test for JEE Main Maths |
| 3 | Online FREE Mock Test for JEE Main Physics |
Important Study Materials Links for JEE Exams
FAQs on Complex Numbers and Quadratic Equations Mock Test for JEE Main 2025-26 Preparation
1. What is a complex number?
A complex number is any number of the form z = a + bi, where a and b are real numbers, and i is the imaginary unit, defined by i² = -1. Here, a is called the real part and b the imaginary part of the complex number.
2. What is the quadratic formula, and how is it used to find roots?
The quadratic formula is used to find the roots of a quadratic equation ax² + bx + c = 0. The roots are given by:
x = (-b ± √(b² - 4ac)) / (2a)
If b² - 4ac (the discriminant) is negative, the equation has complex roots. This formula helps solve any quadratic equation efficiently.
3. How do you represent complex numbers on the Argand plane?
A complex number z = a + bi is graphically represented on the Argand plane (complex plane), where the x-axis shows the real part (a) and the y-axis shows the imaginary part (b). Each complex number corresponds to a unique point (a, b) in this plane.
4. What is the modulus and argument of a complex number?
The modulus of a complex number z = a + bi is |z| = √(a² + b²) and measures its distance from the origin in the Argand plane. The argument (arg(z)) is the angle (θ) the line joining the origin and the point (a, b) makes with the positive real axis, calculated as θ = tan−1(b/a).
5. What are the different methods to solve quadratic equations?
Quadratic equations can be solved by several methods:
1. Factorization (splitting middle term)
2. Completing the square
3. Quadratic formula
4. Graphical method
The choice depends on the equation and convenience, but all methods will yield correct roots.
6. What is the discriminant and what does it indicate about the roots?
The discriminant of a quadratic equation ax² + bx + c = 0 is D = b² - 4ac. It indicates:
• D > 0: Roots are real and distinct
• D = 0: Roots are real and equal
• D < 0: Roots are complex (conjugate pair)
7. How do you add and subtract complex numbers?
To add or subtract complex numbers, separately add or subtract their real parts and imaginary parts.
If z1 = a + bi and z2 = c + di, then:
z1 + z2 = (a + c) + (b + d)i
z1 - z2 = (a - c) + (b - d)i
8. What is a quadratic equation?
A quadratic equation is a second-degree polynomial equation in one variable, generally written as ax² + bx + c = 0, where a ≠ 0, b and c are real numbers. The solutions to this equation are called the roots of the quadratic equation.
9. What is the conjugate of a complex number?
The conjugate of a complex number z = a + bi is ̅z = a - bi. Conjugates have the same real part but opposite signs for the imaginary part. Multiplying a complex number by its conjugate always results in a real number.
10. How do you multiply and divide complex numbers?
To multiply complex numbers, expand as you would binomials and use i² = -1:
For z₁ = a + bi, z₂ = c + di:
z₁ × z₂ = (ac - bd) + (ad + bc)i
To divide, multiply the numerator and denominator by the conjugate of the denominator.
z₁ / z₂ = [(a + bi)(c - di)] / [(c + di)(c - di)], and simplify.
11. Can quadratic equations have imaginary roots? Explain.
Yes, quadratic equations can have imaginary roots if the discriminant (b² - 4ac) is negative. In such cases, the solutions are complex conjugate pairs of the form p ± qi, where both p and q are real numbers.
12. How can you express a complex number in polar form?
A complex number z = a + bi can be written in polar form as z = r(cos θ + i sin θ), where r is the modulus (√(a² + b²)) and θ is the argument (tan−1(b/a)). The polar form is especially useful for multiplication and division of complex numbers.
