Proven Strategies to Ace Complex Numbers & Quadratic Equations in JEE Main Mock Tests
Mastering Complex Numbers and Quadratic Equations is vital for cracking high-scoring Maths questions in JEE Main and Advanced. This chapter delves deep into imaginary and real number systems, quadratic roots, polynomial equations, and their geometric representations. Take this mock test to reinforce your conceptual clarity and problem-solving speed for JEE success!
Mock Test Instructions for the Complex Numbers And Quadratic Equations:
- 20 questions from Complex Numbers And Quadratic Equations
- 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?
- Practice with mock tests to identify recurring mistakes in modulus and argument calculations.
- Evaluate your grasp on quadratic root properties and complex conjugate pairs under timed conditions.
- Understand geometric representations of complex numbers through varied MCQs.
- Strengthen the application of the quadratic formula and Vieta’s relations for faster solutions.
- Improve your accuracy with extensive practice on transformation and polynomial equations involving complex numbers.
Boost Your JEE Maths Score: Expert-Designed Mock Tests on Complex Numbers & Quadratic Equations
- Expertly crafted questions simulate exact JEE exam patterns on quadratic equations and complex number theory.
- Pinpoint weaknesses in roots of unity and graphical solutions through consistent self-assessment.
- Develop precise strategies for tackling problems involving imaginary and real number components.
- Improve retention of critical formulas for quadratic and complex polynomials by repeated mock test attempts.
- Build confidence in problem-solving with feedback-based progress tracking for every core concept.
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 JEE Main 2025-26 Mock Test Practice
1. What is a complex number?
A complex number is a number in the form z = a + ib, where a and b are real numbers, and i is the imaginary unit, defined as i = √(-1). a is called the real part and b is the imaginary part of the complex number.
2. How do you represent a complex number geometrically?
A complex number can be represented as a point or a vector in the Argand plane (also called the complex plane), where the x-axis indicates the real part and the y-axis indicates the imaginary part.
3. What is the conjugate of a complex number?
The conjugate of a complex number z = a + ib is z̄ = a - ib. The conjugate is obtained by changing the sign of the imaginary part while keeping the real part unchanged.
4. What is the modulus of a complex number?
The modulus (or absolute value) of a complex number z = a + ib is written as |z| and is calculated using the formula |z| = √(a² + b²). The modulus gives the distance of the point from the origin in the Argand plane.
5. How do you add and subtract complex numbers?
To add or subtract complex numbers, combine their real parts and imaginary parts separately. For example, (a + ib) + (c + id) = (a + c) + i(b + d).
6. How do you find the roots of a quadratic equation in the form ax²+bx+c=0?
The roots of a quadratic equation ax² + bx + c = 0 are found using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. If (b² - 4ac) < 0, the roots are complex (imaginary) and are written as α ± iβ.
7. What is the principle of argument for a complex number?
The argument of a complex number z = a + ib is the angle θ that the line joining z to the origin makes with the positive real axis. It is calculated as arg(z) = tan⁻¹(b/a).
8. Can every quadratic equation have real roots?
Not every quadratic equation has real roots. The roots are real and distinct if (b² - 4ac) > 0, real and equal if (b² - 4ac) = 0, and complex (imaginary) if (b² - 4ac) < 0.
9. How do you multiply and divide complex numbers?
To multiply (a + ib) and (c + id), use distributive property:
- Multiply the numbers as binomials.
- Replace i² with -1.
Division is done by multiplying numerator and denominator by the conjugate of the denominator and simplifying.
10. What are the different forms of a complex number?
A complex number can be expressed in several equivalent forms:
- Cartesian form: a + ib
- Polar form: r(cosθ + i sinθ), where r = |z| and θ = arg(z)
- Exponential form: r eiθ
11. What is the significance of the discriminant in a quadratic equation?
The discriminant (D) of a quadratic equation ax² + bx + c = 0 is D = b² - 4ac. It determines the nature of the roots:
- D > 0: Two distinct real roots
- D = 0: One repeated real root
- D < 0: Two complex conjugate roots
12. How is the sum and product of quadratic equation roots defined?
For the quadratic equation ax² + bx + c = 0:
- Sum of roots (α + β) = -b/a
- Product of roots (αβ) = c/a
This relationship holds true for both real and complex roots.
