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# 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



Option A: 4√2

Option B: 4

Option C: 2√2

Option D: 2

Option C: 2√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 ________.



Correct Ans: 4

Complex Numbers Problems for Class 12 JEE Questions No: 63

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



Correct Ans: 3

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



Option A: has infinitely many elements

Option B: is a singleton

Option C: has exactly three elements

Option D: has exactly two elements

Option A: has infinitely many solutions

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 ______________.



Correct Ans : 0

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



Option A: 1/2

Option B: 2

Option C: 4

Option D: 1/4

Option A: 1/2

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 _______________.



Correct Ans: 6

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 _________.



Correct Ans: 98

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 _________.



Correct Ans: 310

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 ________.



Correct Ans: 10

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 _________.



Correct Ans: 48

Complex Numbers Questions with Solutions No: 72

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



Option A: 2

Option B: 8

Option C: 3

Option D: √5

Option A: 1/2

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 _______.



Correct Ans: 4

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



Option A: 8

Option B: 7

Option C: 6

Option D: 5

Option B: 7

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



Correct Ans: 1

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 ________.



Correct Ans: 1

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 _____.



Correct Ans: 13

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 ________.



Correct Ans: 6

Complex Numbers Problems for Class 12 JEE Questions No: 79

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



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

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



Option A: 2√2 – 1

Option B: 3√2

Option C: 6√2

Option D: 2√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 _________.