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*.

### JEE Mains Mathematics Complex Numbers Questions Bank

**Complex Numbers Problems for Class 12 JEE Questions No: 31**

A value of θ for which (2 + 3isinθ) / (1 – 2isinθ) is purely imaginary, is

**[2016]**

**Option A**: π/6

**Option B**: sin^{-1}(√3/4)

**Option C**: sin^{-1}(1/√3)

**Option D**: π/3

**Show/Hide Answer Key**

**Option C: sin ^{-1}(1/√3)**

**JEE Complex Numbers Questions No: 32**

The point represented by (2 + i) in Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there 2√2 units in the south-westwards direction. Then its new position in the Argand plane is at the point represented by

**[2016]**

**Option A**: 1 + i

**Option B**: 2 + 2i

**Option C**: -2 – 2i

**Option D**: -1 – i

**Show/Hide Answer Key**

**Option A: 1 + i**

**JEE Main Complex Numbers Questions No: 34**

Let ω be a complex number such that 2ω + 1 = z where z = √-3, if

, then k is equal to

**[2017]**

**Option A**: -z

**Option B**: z

**Option C**: -1

**Option D**: 1

**Show/Hide Answer Key**

**Option A: -z**

**JEE Mathematics Complex Numbers Questions No: 34**

If α, β ∈ C are the distinct roots of the equation x^{2} – x + 1 = 0, then α^{107 }+ β^{107} is equal to

**[2018]**

**Option A**: 2

**Option B**: -1

**Option C**: 0

**Option D**: 1

**Show/Hide Answer Key**

**Option D: 1**

**JEE Main Math Complex Numbers Questions No: 35**

The least positive integer n for which [(1 + i√3) / (1 – i√3)]^{n} = 1, is

**[2018]**

**Option A**: 2

**Option B**: 6

**Option C**: 5

**Option D**: 3

**Show/Hide Answer Key**

**Option D: 3**

**Complex Numbers JEE Questions No: 36**

The set of all α ∈ R for which ω = (1 + (1 – 8)α)z is a purely imaginary number, for all z ∈ C satisfying |z| = 1 and Re(z) ≠ 1 is

**[2018]**

**Option A**: {0}

**Option B**: an empty set

**Option C**: {0, 1/4, -1/4}

**Option D**: equal to R

**Show/Hide Answer Key**

**Option A: {0}**

**Complex Numbers JEE Main Questions No: 37**

Let A = {θ ∈ (-π/2, π) : (3 + 2isinθ) / (1 – 2isinθ) is purely imaginary}. Then, the sum of the elements in A is

**[2019]**

**Option A**: 5π/6

**Option B**: π

**Option C**: 3π/4

**Option D**: 2π/3

**Show/Hide Answer Key**

**Option D: 2π/3**

**Complex Numbers Questions for JEE Mains Questions No: 38**

Let z = (√3/2 + i/2)^{5} + (√3/2 – i/2)^{5}. If Re(z) and Im(z) respectively denote the real and imaginary parts of z, then

**[2019]**

**Option A**: Im(z) = 0

**Option B**: Re(z) > 0 and Im(z) > 0

**Option C**: Re(z) < 0 and Im(z) > 0

**Option D**: Re(z) = -c

**Show/Hide Answer Key**

**Option A: Im(z) = 0**

**Complex Numbers Questions and Answers No: 39**

Let (-2 – i/3)^{3} = (x + iy) / 27, where x and y are real numbers then y – x equals

**[2019]**

**Option A**: 91

**Option B**: -85

**Option C**: 85

**Option D**: -91

**Show/Hide Answer Key**

**Option A: 91**

**Complex Numbers Questions with Solutions No: 40**

If z = (√3/2 + i/2), then (1 + iz + z^{5} + iz^{8})^{9} equal to

**[2019]**

**Option A**: 0

**Option B**: 1

**Option C**: (-1 + 2i)^{9}

**Option D**: -1

**Show/Hide Answer Key**

**Option D: -1**

**JEE Mains Complex Numbers Questions No: 41**

Let z ∈ C be such that |z| < 1. If ω = (5 + 3z) / 5(1 – z), then

**[2019]**

**Option A**: 5Re(ω) > 4

**Option B**: 4Im(ω) > 4

**Option C**: 5Re(ω) > 1

**Option D**: 5Im(ω) < 1

**Show/Hide Answer Key**

**Option C: 5Re(ω) > 1**

**JEE Mains Math Complex Numbers Questions No: 42**

If z and ω are two complex numbers such that |zω| = 1 and arg(z) – arg(ω) = π/2, then

**[2019]**

**Option A**: zω = i

**Option B**: zω = (-1 + i) / √2

**Option C**: zω = -i

**Option D**: zω = (1 – i) / √2

**Show/Hide Answer Key**

**Option C: zω = -i**

**Complex Numbers Questions for JEE Questions No: 43**

Let z_{1} and z_{2} be any two non-zero complex numbers such that 3|z_{1}| = 4|z_{2}|. If z = 3z_{1}/2z_{2} + 2z_{2}/3z_{1}, then

**[2019]**

**Option A**: Re(z) = 0

**Option B**: |z| = √(5/2)

**Option C**: |z| = (1/2)√(17/2)

**Option D**: Im(z) = 0

**Show/Hide Answer Key**

**Option **

**Complex Numbers Problems for Class 11 Questions No: 44**

Let z be a complex number such that |z| + z = 3 + i, where i = √-1. Then |z| is equal to

**[2019]**

**Option A**: √34 / 3

**Option B**: 5/3

**Option C**: √41 / 4

**Option D**: 5 / 4

**Show/Hide Answer Key**

**Option B: 5/3**

**Complex Numbers Problems for Class 12 Questions No: 45**

Let z_{1} and z_{2} be two complex numbers satisfying |z_{1}| = 9 and |z_{2}| – |3| – |4i| = |4|. Then, the minimum value of |z_{1} – z_{2}| is

**[2019]**

**Option A**: 0

**Option B**: √2

**Option C**: 1

**Option D**: 2

**Show/Hide Answer Key**

**Option A: 0**

**Complex Numbers Problems for Class 11 JEE Questions No: 46**

If (z – α) / (z + α) (α ∈ R) is purely imaginary number and |z| = 2, then a value of α is

**[2019]**

**Option A**: 2

**Option B**: 1

**Option C**: 1/2

**Option D**: √2

**Show/Hide Answer Key**

**Option A: 2**

**Complex Numbers Problems for Class 12 JEE Questions No: 47**

If a > 0 and z = (1 + i)^{2} / (a – i), has magnitude √2/5, then z is equal to

**[2019]**

**Option A**: -1/5 – 3i/5

**Option B**: -3/5 – i/5

**Option C**: 1/5 – 3i/5

**Option D**: -1/5 + 3i/5

**Show/Hide Answer Key**

**Option A: -1/5 – 3i/5**

**JEE Complex Numbers Questions No: 48**

Let z ∈ C with Im(z) = 10 and it satisfies (2z – n) / (2z + n) = 2i – 1 for some natural number n. Then,

**[2019]**

**Option A**: n = 20 and Re(z) = -10

**Option B**: n = 40 and Re(z) = 10

**Option C**: n = 40 and Re(z) = -10

**Option D**: n = 20 and Re(z) = 10

**Show/Hide Answer Key**

**Option C: n = 40 and Re(z) = -10**

**JEE Main Complex Numbers Questions No: 49**

The equation |z – i| = |z – 1|, i = √-1, represents:

**[2019]**

**Option A**: a circle of radius 1/2

**Option B**: the line through the origin with slope 1

**Option C**: a circle of radius 1

**Option D**: the line through the origin with slope -1

**Show/Hide Answer Key**

**Option B: the line through the origin with slope 1**

**JEE Mathematics Complex Numbers Questions No: 50**

If Re[(z – 1) / (2z + i)] = 1, where z = x + iy, then the point (x, y) lies on a:

**[2020]**

**Option A**: circle whose center is at (-1/2, -3/2)

**Option B**: straight line whose slope is -2/3

**Option C**: straight line whose slope is 3/2

**Option D**: circle whose diameter is √5/2

**Show/Hide Answer Key**

**Option D: circle whose diameter is √5/2**

**JEE Main Math Complex Numbers Questions No: 51**

Let α = (-1 + i√3) / 2. If and , then a and b are the roots of the quadratic equation

**[2020]**

**Option A**: x^{2} + 101x + 100 = 0

**Option B**: x^{2} – 102x + 101 = 0

**Option C**: x^{2} – 101x + 100 = 0

**Option D**: x^{2} + 102x + 101 = 0

**Show/Hide Answer Key**

**Option B: x ^{2} – 102x + 101 = 0**

**Complex Numbers JEE Questions No: 52**

The imaginary part of (3 + 2√-54)^{1/2} – (3 – 2√-54)^{1/2} can be

**[2020]**

**Option A**: –√6

**Option B**: -2√6

**Option C**: 6

**Option D**: √6

**Show/Hide Answer Key**

**Option B: -2√6**

**Complex Numbers JEE Main Questions No: 53**

The value of is

**[2020]**

**Option A**: (1/2)(1 – i√3)

**Option B**: (1/2)(√3 – i)

**Option C**: -(1/2)(√3 – i)

**Option D**: -(1/2)(1 – i√3)

**Show/Hide Answer Key**

**Option C: –(1/2)(√3 – i)**

**Complex Numbers Questions for JEE Mains Questions No: 54**

If a and b are real numbers such that (2 + α)^{4} = a + bα, where α = (-1 + i√3) / 2, then a + b is

**[2020]**

**Option A**: 9

**Option B**: 24

**Option C**: 33

**Option D**: 57

**Show/Hide Answer Key**

**Option A: 9**

**Complex Numbers Questions and Answers No: 55**

Let z = x + iy be a non-zero complex number such that z^{2} = i|z|^{2}, where i = √-1, then z lies on the

**[2020]**

**Option A**: line y = -x

**Option B**: imaginary axis

**Option C**: line, y = x

**Option D**: real axis

**Show/Hide Answer Key**

**Option C: line y = x**

**Complex Numbers Questions with Solutions No: 56**

If (3 + isinθ) / (4 – icosθ), θ ∈ [0, 2π] is a real number, then an argument of sinθ + icosθ is

**[2020]**

**Option A**: π – tan^{-1}(4/3)

**Option B**: π – tan^{-1}(3/4)

**Option C**: -tan^{-1}(3/4)

**Option D**: tan^{-1}(4/3)

**Show/Hide Answer Key**

**Option B: π – tan ^{-1}(3/4)**

**JEE Mains Complex Numbers Questions No: 57**

If z be a complex number satisfying |Re(z)| + |Im(z)| = 4, then |z| cannot be equal to

**[2020]**

**Option A**: √17/2

**Option B**: √10

**Option C**: √7

**Option D**: √8

**Show/Hide Answer Key**

**Option C: √7**

**JEE Mains Math Complex Numbers Questions No: 58**

Let z be a complex number such that |(z – i) / (z + 2i)| = 1 and |z| = 5/2. Then, the value of |z + 3i| is

**[2020]**

**Option A**: √10

**Option B**: 7/2

**Option C**: 15/4

**Option D**: 2√3

**Show/Hide Answer Key**

**Option B: 7/2**

**Complex Numbers Questions for JEE Questions No: 59**

If z_{1}, z_{2} are complex numbers such that Re(z_{1}) = |z_{1} – 1|, Re(z_{2}) = |z_{2} – 1| and arg(z_{1} – z_{2}) = π / 6, then Im(z_{1} + z_{2}) is equal to

**[2020]**

**Option A**: 2/√3

**Option B**: 2√3

**Option C**: √3/2

**Option D**: 1/√3

**Show/Hide Answer Key**

**Option B: 2√3**

**Complex Numbers Problems for Class 11 Questions No: 60**

The value of ((-1 + i√3) / (1 – i))^{30} is

**[2020]**

**Option A**: -2^{15}

**Option B**: 2^{15}i

**Option C**: -2^{15}i

**Option D**: 6^{5}

**Show/Hide Answer Key**

**Option C: -2 ^{15}i**

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 | |