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

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

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: – ????

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

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

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 A: a² = b

Option B: a² = 2b

Option C: a² = 3b

Option D: a² = 4b

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

Complex Numbers Questions and Answers No: 8

If z = x – iy and z^1/3 = 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

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

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: -π

Option C: 0

Option D: -π/2

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

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

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

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

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

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)

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

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

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)

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

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

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

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]

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

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}

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

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

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

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

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