EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 29 June 2022 Shift 2>Q 91

MEDIUM

JEE Main

IMPORTANT

Earn 100

Let $(z)$ represent the principal argument of the complex number $z$ . Then, $|z| = 3$ and $\arg (z - 1) - \arg (z + 1) = \frac{π}{4}$ intersect:

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Important Questions on Complex Numbers

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 25 July 2022 Shift 1>Q 92

If

α, β, γ, δ

are the roots of the equation

x^{4} + x^{3} + x^{2} + x + 1 = 0

, then

α^{2021} + β^{2021} + γ^{2021} + δ^{2021}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 25 July 2022 Shift 1>Q 93

For

n \in N

, let

S_{n} = \{z \in C : |z - 3 + 2 i| = \frac{n}{4}\}

and

T_{n} = \{z \in C : |z - 2 + 3 i| = \frac{1}{n}\}

. Then the number of elements in the set

\{n \in N : S_{n} \cap T_{n} = ϕ\}

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 25 July 2022 Shift 2>Q 94

For

z \in ℂ

if the minimum value of

(|z - 3 \sqrt{2}| + |z - p \sqrt{2} i|)

is

5 \sqrt{2}

, then a value of

p

is _______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 26 July 2022 Shift 1>Q 95

Let

O

be the origin and

A

be the point

z_{1} = 1 + 2 i

. If

B

is the point

z_{2}, Re (z_{2}) < 0

, such that

O A B

is a right angled isosceles triangle with

O B

as hypotenuse, then which of the following is NOT true?

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 26 July 2022 Shift 2>Q 96

If

z = x + i y

satisfies

|z| - 2 = 0

and

|z - i| - |z + 5 i| = 0

, then

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 27 July 2022 Shift 1>Q 97

Let the minimum value

v_{0}

of

v = {|z|}^{2} + {|z - 3|}^{2} + {|z - 6 i|}^{2}

,

z \in ℂ

is attained at

z = z_{0}

. Then

{|2 z_{0}^{2} - {\bar{z}}_{0}^{3} + 3|}^{2} + v_{0}^{2}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 27 July 2022 Shift 1>Q 98

Let

S = \{z \in ℂ : z^{2} + \bar{z} = 0\}

. Then

\sum_{z \in S} (Re (z) + Im (z))

is equal to _______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 27 July 2022 Shift 2>Q 99

Let

S

be the set of all

(α, β), π < α, β < 2 π

, for which the complex number

\frac{1 - i \sin α}{1 + 2 i \sin α}

is purely imaginary and

\frac{1 + i \cos β}{1 - 2 i \cos β}

is purely real. Let

Z_{α β} = \sin 2 α + i \cos 2 β, (α, β) \in S

.
Then

\sum_{(α, β) \in S} (i Z_{α β} + \frac{1}{i {\bar{Z}}_{α β}})

is equal to