JEE Math Previous Year Paper Complex Numbers Questions Answer Keys Solutions

Welcome to AMBiPi (Read as: एम्बीपाई) (Amans Maths Blogs). JEE Mains and JEE Advanced exams are the engineering entrance exams for taking admission in IITs, NITs and other engineering colleges. In this article, you will get JEE Main Mathematics Previous Paper Complex Numbers Questions Answer Keys Solutions.

Complex Numbers Problems for Class 12 Questions No: 61

If the four complex numbers z, z, z – 2Re(z) and z – 2Re(z) represents the vertices of a square of side 4 units in the argand plane, then |z| is equal to 

[2020]

Option A: 4√2

Option B: 4

Option C: 2√2

Option D: 2

Complex Numbers Problems for Class 11 JEE Questions No: 62

If ((1 + i) / (1 – i))^m/2 = ((1 + i) / (1 – i))^n/3 = 1 (m, n ∈ N), then the greatest common divisor of the least values of m and n is ________.

[2020]

The sum of 162^nd power of the roots of the equation x³ – 2x² + 2x – 1 = 0 is _________.

[2021]

JEE Complex Numbers Questions No: 64

Let S₁, S₂ and S₃ be three sets defined as S₁ = {z ∈ C : |z – 1|*√2} S₂ = {z ∈ C : Re((1 – i)z) ≥ 1} S₃ = {z ∈ C : Im(z) ≥ 1}. Then, the set S₁ ∩ S₂ ∩ S₃

[2021]

Option A: has infinitely many elements

Option B: is a singleton

Option C: has exactly three elements

Option D: has exactly two elements

JEE Main Complex Numbers Questions No: 65

If f(x) and g(x) are two polynomials such that the polynomials p(x) = f(x)³ + x(x³) is divisible by x² + x + 1, then p(1) is equal to ______________.

[2021]

JEE Mathematics Complex Numbers Questions No: 66

Let a complex number be w = 1 – √3i. Let another complex number z be such that |zw| = 1 and arg(z) – arg(w) = π/2. Then the area of the triangle with vertices origin, z and w is equal to

[2021]

Option A: 1/2

Option B: 2

Option C: 4

Option D: 1/4

JEE Main Math Complex Numbers Questions No: 67

Let z₁, z₂ be the roots of the equation z² + az + 12 = 0 and z₁, z₂ form an equilateral triangle with origin. Then, the value of |a| is _______________.

[2021]

Complex Numbers JEE Questions No: 68

A point z moves in the complex plane such that arg((z – 2) / (z + 2)) = π/4, then the minimum value of |z – 9√2 – 2i| is equal to _________.

[2021]

Complex Numbers JEE Main Questions No: 69

Let i = √-1. If , and n = [|k|] be the greatest integral part of |k|. Then is equal to _________.

[2021]

Complex Numbers Questions for JEE Mains Questions No: 70

If the least and the largest real values of α, for which the equation z + α|z – 1| + 2i = 0 (z ∈ C and i = √-1) has a solution, are p and q respectively, then 4(p² + q²) is equal to ________.

[2021]

Complex Numbers Questions and Answers No: 71

Let z be those complex numbers which satisfy |z + 5| ≤ 4 and z(1 + i) + z(1 – i) ≥ -10, i = √-1. If the maximum value of |z + 1|2 is α + β√2, then the value of (α + β) is _________.

[2021]

Complex Numbers Questions with Solutions No: 72

The least value of |z| where z is complex number which satisfies the inequality is equal to

[2021]

Option A: 2

Option B: 8

Option C: 3

Option D: √5

JEE Mains Complex Numbers Questions No: 73

Let z and w be two complex numbers such that w = zz – 2z + 2, |(z + i) / (z – 3i)| = 1 and Re(w) has minimum value. Then, the minimum value of n ∈ N for which wⁿ is real, is equal to _______.

[2021]

JEE Mains Math Complex Numbers Questions No: 74

Let a complex number z, |z| ≠ 1, satisfy . Then, the largest value of |z| is equal to 

[2021]

Option A: 8

Option B: 7

Option C: 6

Option D: 5

Complex Numbers Questions for JEE Questions No: 75

If the real part of the complex number z = (3 + 2icosθ) / (1 – 3icosθ), θ ∈ (0, π/2) is zero, then the value of sin²3θ + cos²θ is equal to

[2021]

Complex Numbers Problems for Class 11 Questions No: 76

The least positive integer n such that (2i)ⁿ / (1 – i)^n-2, i = √-1 is a positive integer, is ________.

[2021]

Complex Numbers Problems for Class 12 Questions No: 77

Let z = (1 – i√3) / 2, i = √-1. Then, the value of 21 + (z + 1/z)³ + (z² + 1/z²)³ + (z³ + 1/z³)³ + … + (z²¹ + 1/z²¹)³ is _____.

[2021]

Complex Numbers Problems for Class 11 JEE Questions No: 78

Let z₁ and z₂ be two complex numbers such that arg(z₁ – z₂) = π/4 and z₁, z₂ satisfy the equation |z – 3| = Re(z). Then, the imaginary part of z₁ + z₂ is equal to ________.

[2021]

Complex Numbers Problems for Class 12 JEE Questions No: 79

If S = {z ∈ C: (z – i) / (z + 2i) ∈ R}, then 

[2021]

Option A: S contains exactly two elements

Option B: S contains only one element

Option C: S is a circle in the complex plane

Option D: S is a straight line in the complex plane

JEE Complex Numbers Questions No: 80

If z is a complex number such that (z – i) / (z – 1) is purely imaginary, then the minimum value of |z – (3 + 3i)| is

[2021]

Option A: 2√2 – 1

Option B: 3√2

Option C: 6√2

Option D: 2√2

JEE Main Complex Numbers Questions No: 81

If for the complex numbers z satisfying |z – 2 – 2i| ≤ 1, then the maximum value of |3iz + 6| is attained at a + ib, then a + b is equal to _________.

[2021]