Complex Numbers JEE Questions PDF with Solution, Practice Now

Complex Numbers JEE Questions: Complex Numbers Chapter for JEE Main and JEE Advanced is a crucial topic of Algebra. Complex numbers involve the numbers of the form a+iba + iba+ib, where i=−1i = \sqrt{-1}i=−1. This chapter enables the learners to understand various properties of imaginary numbers, modulus and argument, and the unity root of a complex number. In JEE Main and JEE Advanced exams, complex numbers are often integrated with Quadratic equations, sequences, and trigonometry.

Complex Numbers JEE Questions Practice is important because it helps to enhance problem-solving speed and accuracy. Solving JEE complex numbers questions helps students to get a good grasp on JEE Advanced complex number problems. The practice also makes students well-versed with the JEE Main exam pattern and types of questions in the JEE exam. Tricky JEE questions for complex numbers are also generally asked in the exam paper.

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Complex Numbers JEE Questions Overview

The complex number chapter includes topics such as addition, multiplication, division, conjugates, modulus, argument, De Moivre’s theorem, roots of unity, and geometric interpretation. For the JEE exam, students may be asked to find the real and imaginary parts, evaluate expressions involving powers of 𝑖, or use complex numbers in geometry problems, such as finding points on circles or regular polygons. Complex numbers JEE Mains questions are usually more formulaic and straightforward, while JEE Advanced complex number problems may involve combining multiple concepts and are generally more difficult. Practicing important complex number JEE Main previous year questions can help aspirants improve their speed, accuracy, and familiarity with all types of questions that may appear in the JEE exams.

Practice Complex Numbers JEE Questions 

Here are some sample Complex Numbers JEE Questions following the JEE exam pattern:

1. The value of sin log(i^4), where i = √(-1), is:

A. 1
B. -1
C. 0
D. 2

2. The real part of (1 – i)^-i is:

A. e^(π/4) cos(ln 2)
B. e^(-π/4) (1/2 cos ln 2)
C. e^(-π/4) cos(1/2 ln 2)
D. e^(π/4) cos(1/2 ln 2)

3. Let f(z) = the real part of z. If a ∈ N, n ∈ N then the value of
Σ (n=1 to 6a) log₂ [f((1 + √-3)^n)] has the value equal to:

A. 18a² + 3a
B. 18a² – 3a
C. 18a² – a
D. 18a² + a

4. If n is a positive integer then (1 + i)^n + (1 – i)^n is:

A. 2^((n+2)/2) cos(nπ/4)
B. 2^((n+2)/2) sin(nπ/4)
C. 2^((n+2)/2) [cos(nπ/4) + i sin(nπ/4)]
D. None of these

5. If x + iy = √[(3 + i)/(1 + 3i)] then (x² + y²)² equals:

A. 0
B. 2
C. 3
D. 1

6. Dividing f(z) by z – i, we obtain the remainder 1 – i and dividing it by z + i, we get the remainder 1 + i. Then, the remainder upon the division of f(z) by z² + 1 is:

A. i + z
B. 1 + z
C. 1 – z
D. None of these

7. z = (3 + 7i)(λ + μi), when λ, μ ∈ I – {0} and i = √(-1), is purely imaginary then minimum value of |z|² is:

A. 0
B. 58
C. 3364/3
D. 3364

8. If |z – i| ≤ 2 and z₀ = 5 + 3i, then the maximum value of |z + z₀| is:

A. 2 + √31
B. √31 – 2
C. 7
D. –7

9. If P(w) lies on the chord joining A, B where A(a), B(b) lie on the unit circle |z| = 1, then ω is equal to:

A. (a + b – ω)/(a + b)
B. (a + b – ω)/(ab)
C. (1/2)(a + b) – (ω/ab)
D. 1/(ab + b + ω)

10. z₁ and z̅₁ represent adjacent vertices of a regular polygon of n sides whose centre is origin and if Im(z₁)/Re(z₁) = √2 – 1, then n is equal to:

A. 8
B. 16
C. 24
D. 32

11. 1/(a + ω) + 1/(b + ω) + 1/(c + ω) + 1/(d + ω) = 1/ω, where a, b, c, d ∈ R and ω is a cube root of unity then Σ 1/(a² – a + 1) is equal to:

A. 1
B. 2
C. 3
D. 1/3

12. If z₁, z₂, z₃ are three points lying on the circle |z| = 2, then the minimum value of |z₁ + z₂|² + |z₂ + z₃|² + |z₃ + z₁|² is equal to:

A. 6
B. 12
C. 8
D. 24

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Complex Numbers JEE Questions PDF with Solution

PW has given the practice question PDF with answers and solutions to ease your preparation. The given PDF is for Complex Numbers JEE Questions. It consists of complex numbers JEE Mains questions and complex number JEE Advanced questions with important complex number PYQs for revision. Students can learn the concepts with the help of the step-by-step solution provided for the questions.