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 Math Previous Year Paper Complex Numbers Questions Answer Keys Solutions*.

### JEE Mains Mathematics Complex Numbers Questions Bank

**JEE Complex Numbers Questions No: 1**

The locus of the center of a circle which touches the circle |z – z_{1}| = a and |z – z_{2}| = b externally (z, z_{1}, z_{2} are complex numbers) will be

**[2002]**

**Option A**: An Ellipse

**Option B**: A Hyperbola

**Option C**: A Circle

**Option D**: None of These

**Show/Hide Answer Key**

**Option B: A Hyperbola**

**JEE Main Complex Numbers Questions No: 2 **

If |z – 4| < |z – 2|, its solution is given by

**[2002]**

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

**Option B**: Re(z) < 0

**Option C**: Re(z) > 3

**Option D**: Re(z) > 2

**Show/Hide Answer Key**

**Option C: Re(z) > 3**

**JEE Mathematics Complex Numbers Questions No: 3 **

z and ???? are two non-zero complex numbers such that |z| = |????| and arg(z) + arg(????) = π, then z equals to

**[2002]**

**Option A**: ????

**Option B**: – ????

**Option C**: ????

**Option D**: – ????

**Show/Hide Answer Key**

**Option B: – ????**

**JEE Main Math Complex Numbers Questions No: 4**

If [ (1 + i) / (1 – i) ]^{x} = 1, then

**[2003]**

**Option A**: x = 4n, where n is any positive integer

**Option B**: x = 2n, where n is any positive integer

**Option C**: x = 4n + 1, where n is any positive integer

**Option D**: x = 2n + 1, where n is any positive integer

**Show/Hide Answer Key**

**Option A: x = 4n, where n is any positive integer**

**Complex Numbers JEE Questions No: 5 **

If z and ???? are two non-zero complex numbers such that |z????| = 1 and arg(z) – are(????) = π/2, then z???? is equal to

**[2003]**

**Option A**: 1

**Option B**: -1

**Option C**: i

**Option D**: -i

**Show/Hide Answer Key**

**Option B: – i**

**Complex Numbers JEE Main Questions No: 6**

Let z_{1} and z_{2} be two roots of the equation z^{2} + az + b = 0, z being complex, Further, assume that the origin z_{1} and z_{2} form an equilateral triangle, then

**[2003]**

**Option A**: a^{2} = b

**Option B**: a^{2} = 2b

**Option C**: a^{2} = 3b

**Option D**: a^{2} = 4b

**Show/Hide Answer Key**

**Option C: a ^{2} = 3b**

**Complex Numbers Questions for JEE Mains Questions No: 7 **

If |z^{2} – 1| = |z|^{2} + 1, then z lies on

**[2004]**

**Option A**: the real axis

**Option B**: an ellipse

**Option C**: a circle

**Option D**: the imaginary

**Show/Hide Answer Key**

**Option C: the imaginary**

**Complex Numbers Questions and Answers No: 8**

If z = x – iy and z^{1/3} = p + iq, then (x/p + y/q) / (p^{2} + q^{2}) is equal to

**[2004]**

**Option A**: 1

**Option B**: -2

**Option C**: 2

**Option D**: -1

**Show/Hide Answer Key**

**Option B: -2**

**Complex Numbers Questions with Solutions No: 9**

Let z, ω be complex numbers such that z + iω = 0 and arg(zω) = π. Then, arg(z) equals

**[2004]**

**Option A**: π/4

**Option B**: 5π/4

**Option C**: 3π/4

**Option D**: π/2

**Show/Hide Answer Key**

**Option C: π/2**

**JEE Mains Complex Numbers Questions No: 10**

If z_{1} and z_{2} are two non-zero complex numbers such that |z_{1} + z_{2}| = |z_{1}| + |z_{2}|, then arg(z_{1}) – arg(z_{2}) is equal to

**[2005]**

**Option A**: π/2

**Option B**: -π

**Option C**: 0

**Option D**: -π/2

**Show/Hide Answer Key**

**Option C: 0**

**JEE Mains Math Complex Numbers Questions No: 11**

If ω = z / (z – i/3) and |ω| = 1, then z lies on

**[2005]**

**Option A**: an ellipse

**Option B**: a circle

**Option C**: a straight line

**Option D**: a parabola

**Show/Hide Answer Key**

**Option C: a straight line**

**Complex Numbers Questions for JEE Questions No: 12**

If the cube roots of unity are 1, ω, ω^{2}, then the roots of the equation (x – 1)^{3} + 8 = 0 are

**[2005]**

**Option A**: -1, -1 + 2ω, -1 – 2ω^{2}

**Option B**: -1, -1, -1

**Option C**: -1, 1 – 2ω, 1- 2ω^{2}

**Option D**: -1, 1 + 2ω, 1 + 2ω^{2}

**Show/Hide Answer Key**

**Option C: -1, 1 – 2ω, 1- 2ω ^{2}**

**Complex Numbers Problems for Class 11 Questions No: 13**

If (z + 1/z)^{2} + (z^{2} + 1/z^{2})2 + (z^{3} + 1/z^{3}) + … + (z^{6} + 1/z^{6})^{2} is

**[2006]**

**Option A**: 18

**Option B**: 54

**Option C**: 6

**Option D**: 12

**Show/Hide Answer Key**

**Option D: 12**

**Complex Numbers Problems for Class 12 Questions No: 14**

The value of

**[2006]**

**Option A**: i

**Option B**: 1

**Option C**: -1

**Option D**: -i

**Show/Hide Answer Key**

**Option D: -i**

**Complex Numbers Problems for Class 11 JEE Questions No: 15**

If |z + 4| ≤ 3, then the maximum value of |z + 1| is

**[2007]**

**Option A**: 4

**Option B**: 10

**Option C**: 6

**Option D**: 0

**Show/Hide Answer Key**

**Option C: 6**

**Complex Numbers Problems for Class 12 JEE Questions No: 16**

The conjugate of a complex number is 1 / (i – 1). Then the complex number is

**[2008]**

**Option A**: -1 / (i – 1)

**Option B**: 1 / (i + 1)

**Option C**: -1 / (i + 1)

**Option D**: 1 / (i – 1)

**Show/Hide Answer Key**

**Option C: -1 / (i + 1)**

**JEE Complex Numbers Questions No: 17**

If |z – 4/z| = 2, then the maximum value of |z| is equal to

**[2009]**

**Option A**: √3 + 1

**Option B**: √5 + 1

**Option C**: 2

**Option D**: 2 + √2

**Show/Hide Answer Key**

**Option B: √5 + 1**

**JEE Main Complex Numbers Questions No: 18**

The number of complex numbers z such that |z – 1| = |z + 1| = |z – 1| equals

**[2010]**

**Option A**: 1

**Option B**: 2

**Option C**: ∞

**Option D**: 0

**Show/Hide Answer Key**

**Option A: 1**

**JEE Mathematics Complex Numbers Questions No: 19**

If ω ≠ 1 is a cube root of unity and ( 1 + ω)^{7} = A + Bω. Then, (A, B) equals

**[2011]**

**Option A**: (1, 1)

**Option B**: (1, 0)

**Option C**: (-1, 1)

**Option D**: (0, 1)

**Show/Hide Answer Key**

**Option A: 1**

**JEE Main Math Complex Numbers Questions No: 20**

If z ≠ 1 and z^{2} / (z – 1) is real, then the point represented by the complex number z lies

**[2012]**

**Option A**: either on the real axis or on a circle passing through the origin

**Option B**: on the imaginary axis

**Option C**: either on the real axis or on a circle passing through the origin

**Option D**: on a circle with centre at the origin

**Show/Hide Answer Key**

**Option C: either on the real axis or on a circle passing through the origin**

**Complex Numbers JEE Main Questions No: 21**

|z_{1} + z_{2}|^{2} + |z_{1} – z_{2}|^{2} equals to

**[2012]**

**Option A**: 2(|z_{1}| + |z_{2}|)

**Option B**: 2(|z_{1}|^{2} + |z_{2}|^{2})

**Option C**: |z_{1}||z_{2}|

**Option D**: |z_{1}|^{2} + |z_{2}|^{2}

**Show/Hide Answer Key**

**Option B: 2(|z _{1}|^{2} + |z_{2}|^{2})**

**Complex Numbers Questions for JEE Mains Questions No: 22**

If z is a complex number of unit modulus and argument θ, then arg(1 + z)/(1 + z) equals

**[2013]**

**Option A**: π/2 – θ

**Option B**: θ

**Option C**: π – θ

**Option D**: – θ

**Show/Hide Answer Key**

**Option B: – θ**

**Complex Numbers Questions and Answers No: 23**

Let a = Im(1 + z^{2}) / (2iz), where z is any non-zero complex number. The set A = {a : |z| = 1 and z = ±1} is equal to

**[2013]**

**Option A**: (-1, 1)

**Option B**: [-1, 1]

**Option C**: [0, 1)

**Option D**: (-1, 0]

**Show/Hide Answer Key**

**Option A: (-1, 1)**

**Complex Numbers Questions with Solutions No: 24**

If z is a complex number such that |z| ≥ 2, then the minimum value of |z + 1/2|

**[2014]**

**Option A**: is equal to 5/2

**Option B**: lies in interval (1, 2)

**Option C**: is strictly greater than 5/2

**Option D**: is strictly greater than 3/2 but less than 5/2

**Show/Hide Answer Key**

**Option B: lies in interval (1, 2)**

**JEE Mains Complex Numbers Questions No: 25**

Let ω (Im ω ≠ 0) be a complex number. Then, the set of all complex number z satisfying the equation ω – ωz = k(1 – z), for some real number k, is

**[2014]**

**Option A**: {z : |z| = 1}

**Option B**: {z : z = z}

**Option C**: {z : z ≠ 1}

**Option D**: {z : |z| = 1, z ≠ 1}

**Show/Hide Answer Key**

**Option D: {z : |z| = 1, z ≠ 1}**

**JEE Mains Math Complex Numbers Questions No: 26**

If z_{1}, z_{2} and z_{3}, z_{4} are pairs of complex conjugate numbers, then arg(z_{1}/z_{4}) + arg(z_{2}/z_{3}) equals

**[2014]**

**Option A**: 0

**Option B**: π/2

**Option C**: 3π/2

**Option D**: π

**Show/Hide Answer Key**

**Option A: 0**

**Complex Numbers Questions for JEE Questions No: 27**

Let z ≠ -i be any complex number such that (z – i) / (z + i) is a purely imaginary number. Then, z + 1/z is

**[2014]**

**Option A**: zero

**Option B**: any non-zero real number other than 1

**Option C**: any non-zero real number

**Option D**: a purely imaginary number

**Show/Hide Answer Key**

**Option C: any non-zero real number**

**Complex Numbers Problems for Class 11 Questions No: 28**

For all complex numbers z of the form 1 + iα, α ∈ R, if z^{2} = x + iy, then

**[2014]**

**Option A**: y^{2} – 4x + 2 = 0

**Option B**: y^{2} + 4x – 4 = 0

**Option C**: y^{2} – 4x – 4 = 0

**Option D**: y^{2} + 4x + 2 = 0

**Show/Hide Answer Key**

**Option B: y ^{2} + 4x – 4 = 0**

**Complex Numbers Problems for Class 12 Questions No: 29**

A complex number z is said to be unimodular if |z| = 1. Suppose z_{1} and z_{2} are complex numbers such that (z_{1} – 2z_{2}) / (2 – z_{1}z_{2})

**[2015]**

**Option A**: straight line parallel to y-axis

**Option B**: circle of radius 2

**Option C**: circle of radius √2

**Option D**: straight line parallel to x-axis

**Show/Hide Answer Key**

**Option B: circle of radius 2**

**Complex Numbers Problems for Class 11 JEE Questions No: 30**

If z is non- real complex number, then the minimum value of Im(z^{5}) / (Im(z))^{5} is

**[2015]**

**Option A**: -1

**Option B**: -4

**Option C**: -2

**Option D**: -5

**Show/Hide Answer Key**

**Option B: -4**

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 | |