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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



Option A: An Ellipse

Option B: A Hyperbola

Option C: A Circle

Option D: None of These

Option B: A Hyperbola

JEE Main Complex Numbers Questions No: 2

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



Option A: Re(z) > 0

Option B: Re(z) < 0

Option C: Re(z) > 3

Option D: Re(z) > 2

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



Option A: ????

Option B: ????

Option C: ????

Option D: – ????

Option B: ????

JEE Main Math Complex Numbers Questions No: 4

If [ (1 + i) / (1 – i) ]x = 1, then



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

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



Option A1

Option B: -1

Option C: i

Option D: -i

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



Option Aa2 = b

Option B: a2 = 2b

Option C: a2 = 3b

Option D: a2 = 4b

Option C: a2 = 3b

Complex Numbers Questions for JEE Mains Questions No: 7

If |z2 – 1| = |z|2 + 1, then z lies on



Option A: the real axis

Option B: an ellipse

Option C: a circle

Option D: the imaginary

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



Option A: 1

Option B: -2

Option C: 2

Option D: -1

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



Option A: π/4

Option B: 5π/4

Option C: 3π/4

Option D: π/2

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



Option A: π/2

Option B:

Option C: 0

Option D: -π/2

Option C: 0

JEE Mains Math Complex Numbers Questions No: 11

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



Option A: an ellipse

Option B: a circle

Option C: a straight line

Option D: a parabola

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



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

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



Option A: 18

Option B: 54

Option C: 6

Option D: 12

Option D: 12

Complex Numbers Problems for Class 12 Questions No: 14

The value of is



Option A: i

Option B: 1

Option C: -1

Option D: -i

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



Option A: 4

Option B: 10

Option C: 6

Option D: 0

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



Option A: -1 / (i – 1)

Option B: 1 / (i + 1)

Option C: -1 / (i + 1)

Option D: 1 / (i – 1)

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



Option A: √3 + 1

Option B: √5 + 1

Option C: 2

Option D: 2 + √2

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



Option A: 1

Option B: 2

Option C: ∞

Option D: 0

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



Option A: (1, 1)

Option B: (1, 0)

Option C: (-1, 1)

Option D: (0, 1)

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



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

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



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

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

Option C: |z1||z2|

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

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



Option A: π/2 – θ

Option B: θ

Option C: π – θ

Option D: – θ

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



Option A: (-1, 1)

Option B: [-1, 1]

Option C: [0, 1)

Option D: (-1, 0]

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|



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

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



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

Option B: {z : z = z}

Option C: {z : z ≠ 1}

Option D: {z : |z| = 1, 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



Option A: 0

Option B: π/2

Option C: 3π/2

Option D: π

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



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

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



Option A: y2 – 4x + 2 = 0

Option B: y2 + 4x – 4 = 0

Option C: y2 – 4x – 4 = 0

Option D: y2 + 4x + 2 = 0

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)



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

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



Option A: -1

Option B: -4

Option C: -2

Option D: -5