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# JEE Main 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 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 – z1| = a and |z – z2| = b externally (z, z1, z2 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

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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 Ax = 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

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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 A1

Option B: -1

Option C: i

Option D: -i

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Option B: – i

Complex Numbers JEE Main Questions No: 6

Let z1 and z2 be two roots of the equation z2 + az + b = 0, z being complex, Further, assume that the origin z1 and z2 form an equilateral triangle, then

[2003]

Option Aa2 = b

Option B: a2 = 2b

Option C: a2 = 3b

Option D: a2 = 4b

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Option C: a2 = 3b

Complex Numbers Questions for JEE Mains Questions No: 7

If |z2 – 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

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Option C: the imaginary

Complex Numbers Questions and Answers No: 8

If z = x – iy and z1/3 = p + iq, then (x/p + y/q) / (p2 + q2) is equal to

[2004]

Option A: 1

Option B: -2

Option C: 2

Option D: -1

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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

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Option C: π/2

JEE Mains Complex Numbers Questions No: 10

If z1 and z2 are two non-zero complex numbers such that |z1 + z2| = |z1| + |z2|, then arg(z1) – arg(z2) is equal to

[2005]

Option A: π/2

Option B:

Option C: 0

Option D: -π/2

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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

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Option C: a straight line

Complex Numbers Questions for JEE Questions No: 12

If the cube roots of unity are 1, ω, ω2, then the roots of the equation (x – 1)3 + 8 = 0 are

[2005]

Option A: -1, -1 + 2ω, -1 – 2ω2

Option B: -1, -1, -1

Option C: -1, 1 – 2ω, 1- 2ω2

Option D: -1, 1 + 2ω, 1 + 2ω2

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Option C: -1, 1 – 2ω, 1- 2ω2

Complex Numbers Problems for Class 11 Questions No: 13

If (z + 1/z)2 + (z2 + 1/z2)2 + (z3 + 1/z3) + … + (z6 + 1/z6)2 is

[2006]

Option A: 18

Option B: 54

Option C: 6

Option D: 12

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Option D: 12

Complex Numbers Problems for Class 12 Questions No: 14

The value of  is

[2006]

Option A: i

Option B: 1

Option C: -1

Option D: -i

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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)

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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

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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)

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Option A: 1

JEE Main Math Complex Numbers Questions No: 20

If z ≠ 1 and z2 / (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

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

Complex Numbers JEE Main Questions No: 21

|z1 + z2|2 + |z1 – z2|2 equals to

[2012]

Option A: 2(|z1| + |z2|)

Option B: 2(|z1|2 + |z2|2)

Option C: |z1||z2|

Option D: |z1|2 + |z2|2

Show/Hide Answer Key

Option B: 2(|z1|2 + |z2|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

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Option B: – θ

Complex Numbers Questions and Answers No: 23

Let a = Im(1 + z2) / (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}

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Option D: {z : |z| = 1, z ≠ 1}

JEE Mains Math Complex Numbers Questions No: 26

If z1, z2 and z3, z4 are pairs of complex conjugate numbers, then arg(z1/z4) + arg(z2/z3) equals

[2014]

Option A: 0

Option B: π/2

Option C: 3π/2

Option D: π

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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

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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 z2 = x + iy, then

[2014]

Option A: y2 – 4x + 2 = 0

Option B: y2 + 4x – 4 = 0

Option C: y2 – 4x – 4 = 0

Option D: y2 + 4x + 2 = 0

Show/Hide Answer Key

Option B: y2 + 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 z1 and z2 are complex numbers such that (z1 – 2z2) / (2 – z1z2)

[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(z5) / (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 |
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