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# JEE Main Mathematics Previous 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 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

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

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

Option A: -z

JEE Mathematics Complex Numbers Questions No: 34

If α, β ∈ C are the distinct roots of the equation x2 – x + 1 = 0, then α107 + β107 is equal to

[2018]

Option A: 2

Option B: -1

Option C: 0

Option D: 1

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

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

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

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

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

Option A: 91

Complex Numbers Questions with Solutions No: 40

If z = (√3/2 + i/2), then (1 + iz + z5 + iz8)9 equal to

[2019]

Option A: 0

Option B: 1

Option C: (-1 + 2i)9

Option D: -1

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

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

Option C: zω = -i

Complex Numbers Questions for JEE Questions No: 43

Let z1 and z2 be any two non-zero complex numbers such that 3|z1| = 4|z2|. If z = 3z1/2z2 + 2z2/3z1, then

[2019]

Option A: Re(z) = 0

Option B: |z| = √(5/2)

Option C: |z| = (1/2)√(17/2)

Option D: Im(z) = 0

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

Option B: 5/3

Complex Numbers Problems for Class 12 Questions No: 45

Let z1 and z2 be two complex numbers satisfying |z1| = 9 and |z2| – |3| – |4i| = |4|. Then, the minimum value of |z1 – z2| is

[2019]

Option A: 0

Option B: √2

Option C: 1

Option D: 2

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

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

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

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

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

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: x2 + 101x + 100 = 0

Option B: x2 – 102x + 101 = 0

Option C: x2 – 101x + 100 = 0

Option D: x2 + 102x + 101 = 0

Option B: x2 – 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

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)

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

Option A: 9

Complex Numbers Questions and Answers No: 55

Let z = x + iy be a non-zero complex number such that z2 = 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

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)

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

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

Option B: 7/2

Complex Numbers Questions for JEE Questions No: 59

If z1, z2 are complex numbers such that Re(z1) = |z1 – 1|, Re(z2) = |z2 – 1| and arg(z1 – z2) = π / 6, then Im(z1 + z2) is equal to

[2020]

Option A: 2/√3

Option B: 2√3

Option C: √3/2

Option D: 1/√3

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: -215

Option B: 215i

Option C: -215i

Option D: 65