Complex Numbers And Quadratic Equations JEE Mains Questions - List Of Most Asked Questions With Solutions

NTA will shortly release the JEE Main Syllabus 2025 at jeemain.nta.ac.in. Last Year, the complete syllabus of JEE Main underwent some major changes. According to the latest syllabus guidelines, the weightage of Maths has dropped to 22.5%. Due to these changes in the syllabus, certain shifts in chapter-wise weightage have been observed. Complex Number and Quadratic Equation are among such topics. It’s among the least weightage topics in JEE Main Maths Syllabus 2025. This chapter holds 1.39% weightage in the whole syllabus.

• Complex Number and Quadratic Equation is a part of the General Maths section, and every year around 2-3 questions are asked from this chapter. Due to the drop in weightage, you can expect 1-2 questions in JEE Main 2025.
• Complex Number and Quadratic Equation in JEE Mains Maths Syllabus 2025 covers all the basic concepts on units and measurements, fundamentals of units, dimensions etc.

Aspirants consider Complex Number and Quadratic Equation as one of the Easiest Chapters in Maths for JEE Main 2025. Even though this chapter has the least weightage in the syllabus, to develop a strong foundation in physics, this particular chapter plays a pivotal role. Hence the candidates need to develop a clear understanding of this chapter. The list of most asked questions from this chapter will help the students with their preparation.

Must Check News on JEE Main Maths:

• How to score 80+ in JEE Main
• JEE Main Physics Syllabus Breakdown

Some of the most important topics for differential equations in JEE Main include:

• Variable separable equations
• Homogeneous differential equations
• Linear differential equations
• Exact differential equations
• Integrating factor method
• Second-order differential equations
• Reduction of order
• Variation of parameters
• Applications in physics and engineering
• Systems of differential equations

Complex Number and Quadratic Equations

JEE Mains Questions-List Of Most Asked Questions With Solutions

In the (JEE) Main, the topic of Physics and Measurement often features questions that have appeared multiple times in previous years. Many questions in this section are either repeated or follow similar patterns, with only minor changes, such as different numerical values or slight modifications in wording.Certain questions have been repeated as many as five times.

Here are some of the most frequently asked and repeated questions:

Question 1:

What is the modulus of the complex number 3 + 4i?

Solution: The correct answer is 5. Explanation: The modulus of a complex number z = a + bi is |z| = √(a² + b²).

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question 2:

If z = 1 + i, then what is z²?

Solution: The correct answer is z² = 2i. Explanation: By squaring the complex number z = 1 + i, we get (1 + i)² = 1 + 2i + i² = 2i.

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question 3:

Solve the quadratic equation x² - 5x + 6 = 0.

Solution: The correct answer is x = 2, x = 3. Explanation: By factoring the equation, we get (x - 2)(x - 3) = 0, so x = 2, 3.

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question 4:

What is the value of the argument of the complex number -1 + i√3?

Solution: The correct answer is 120°. Explanation: The argument of a complex number z = a + bi is the angle θ made with the positive real axis. Here, θ = arctan(√3 / -1) = 120°.

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question 5:

If z = 2 - 3i, what is the conjugate of z?

Solution: The correct answer is 2 + 3i. Explanation: The conjugate of a complex number z = a + bi is a - bi.

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question 6:

What are the roots of the quadratic equation x² + 2x + 1 = 0?

Solution: The correct answer is x = -1 (double root). Explanation: The equation can be written as (x + 1)² = 0, so x = -1 is the repeated root.

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question 7:

If z = cosθ + i sinθ, what is the value of z²?

Solution: The correct answer is z² = cos2θ + i sin2θ. Explanation: Using De Moivre's theorem, (cosθ + i sinθ)² = cos2θ + i sin2θ.

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question 8:

What is the nature of roots for the quadratic equation x² - 4x + 8 = 0?

Solution: The correct answer is Complex roots. Explanation: The discriminant is Δ = b² - 4ac = -16, so the roots are complex.

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question 9:

Solve the quadratic equation x² + 3x + 2 = 0.

Solution: The correct answer is x = -1, x = -2. Explanation: Factoring the equation, we get (x + 1)(x + 2) = 0, so x = -1, -2.

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)

Question 10:

What is the modulus of the complex number -5 + 12i?

Solution: The correct answer is 13. Explanation: The modulus of a complex number z = a + bi is |z| = √(a² + b²), so |z| = 13.

(This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024)