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

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**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 ________.

**[2020]**

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**Correct Ans: 4**

**Complex Numbers Problems for Class 12 JEE Questions No: 63**

The sum of 162^{nd} power of the roots of the equation x^{3} – 2x^{2} + 2x – 1 = 0 is _________.

**[2021]**

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**Correct Ans: 3**

**JEE Complex Numbers Questions No: 64**

Let S_{1}, S_{2} and S_{3} be three sets defined as S_{1} = {z ∈ C : |z – 1|*√2} S_{2} = {z ∈ C : Re((1 – i)z) ≥ 1} S_{3} = {z ∈ C : Im(z) ≥ 1}. Then, the set S_{1} ∩ S_{2} ∩ S_{3}

**[2021]**

**Option A**: has infinitely many elements

**Option B**: is a singleton

**Option C**: has exactly three elements

**Option D**: has exactly two elements

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**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(x^{3}) is divisible by x^{2} + x + 1, then p(1) is equal to ______________.

**[2021]**

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**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

**[2021]**

**Option A**: 1/2

**Option B**: 2

**Option C**: 4

**Option D**: 1/4

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**Option A: 1/2**

**JEE Main Math Complex Numbers Questions No: 67**

Let z_{1}, z_{2} be the roots of the equation z^{2} + az + 12 = 0 and z_{1}, z_{2} form an equilateral triangle with origin. Then, the value of |a| is _______________.

**[2021]**

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**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 _________.

**[2021]**

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**Correct Ans: 98**

**Complex Numbers JEE Main Questions No: 69**

Let i = √-1. If

**[2021]**

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**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(p^{2} + q^{2}) is equal to ________.

**[2021]**

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**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 _________.

**[2021]**

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**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

**[2021]**

**Option A**: 2

**Option B**: 8

**Option C**: 3

**Option D**: √5

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**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 w^{n} is real, is equal to _______.

**[2021]**

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**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

**[2021]**

**Option A**: 8

**Option B**: 7

**Option C**: 6

**Option D**: 5

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**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 sin^{2}3θ + cos^{2}θ is equal to

**[2021]**

**Show/Hide Answer Key**

**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 ________.

**[2021]**

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**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} + (z^{2} + 1/z^{2})^{3} + (z^{3} + 1/z^{3})^{3} + … + (z^{21} + 1/z^{21})^{3} is _____.

**[2021]**

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**Correct Ans: 13**

**Complex Numbers Problems for Class 11 JEE Questions No: 78**

Let z_{1} and z_{2} be two complex numbers such that arg(z_{1} – z_{2}) = π/4 and z_{1}, z_{2} satisfy the equation |z – 3| = Re(z). Then, the imaginary part of z_{1} + z_{2} is equal to ________.

**[2021]**

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**Correct Ans: 6**

**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

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**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

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**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]**

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**Correct Ans: 5**

JEE Main Mathematics Previous Year Questions with Solutions: Algebra |

JEE Main Previous Year Mathematics Questions Set, Relations & Functions | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Complex Numbers | 1 to 30 | 31 to 60 | 61 to 81 | |

JEE Main Previous Year Mathematics Questions Sequence & Series| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Quadratic Equations| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Permutations & Combinations| 1 to 30 | 31 to 60 | 61 to 94 | |

JEE Main Previous Year Mathematics Questions Binomial Theorems| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Determinants & Matrices| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Trigonometry |

JEE Main Previous Year Mathematics Questions Trigonometry Ratios Identities| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Properties of Triangles| 1 to 31 | |

JEE Main Previous Year Mathematics Questions Trigonometrical Equations| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Inverse Trigonometrical Functions| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Height & Distance| 1 to 27 | |

JEE Main Mathematics Previous Year Questions with Solutions: Coordinate Geometry |

JEE Main Previous Year Mathematics Questions Cartesian System & Straight Lines | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Circles | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Parabola | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Ellipse | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Hyperbola | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Differential Equations |

JEE Main Previous Year Mathematics Questions Limit, Continuity & Differentiability | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Differentiations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Application of Derivative | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Integral Calculus |

JEE Main Previous Year Mathematics Questions Indefinite Integrals | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Definite Integrals | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Area By Integration | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Differential Equations |

JEE Main Previous Year Mathematics Questions Differential Equations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Vector & 3D Geometry |

JEE Main Previous Year Mathematics Questions Vectors | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 139 | |

JEE Main Previous Year Mathematics Questions 3D Geometry | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Statistics & Probability |

JEE Main Previous Year Mathematics Questions Statistics | 1 to 30 | 31 to 60 | 61 to 86 | |

JEE Main Previous Year Mathematics Questions Probability | 1 to 30 | 31 to 60 | 61 to 95 | |

JEE Main Mathematics Previous Year Questions with Solutions: Miscellaneous |

JEE Main Previous Year Mathematics Questions Mathematical Induction | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Mathematical Reasoning | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |