EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 24 June 2022 Shift 1>Q 78

MEDIUM

JEE Main

IMPORTANT

Earn 100

Let $A = \{z \in C : 1 ⩽ |z - (1 + i)| ⩽ 2\}$ and $B = \{z \in A : |z - (1 - i)| = 1\}$ . Then, $B$

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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 - 24 June 2022 Shift 2>Q 79

Let

S =

{

z \in ℂ : |z - 3| \leq 1

and

z (4 + 3 i) + \bar{z} (4 - 3 i) \leq 24

}. If

α + i β

is the point in

S

which is closest to

4 i

, then

25 (α + β)

is equal to ______.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 25 June 2022 Shift 1>Q 80

Let a circle

C

in complex plane pass through the points

z_{1} = 3 + 4 i, z_{2} = 4 + 3 i

and

z_{3} = 5 i

. If

z (\neq z_{1})

is a point on

C

such that the line through

z

and

z_{1}

is perpendicular to the line through

z_{2}

and

z_{3}

, then

\arg (z)

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 25 June 2022 Shift 2>Q 81

Let

z_{1}

and

z_{2}

be two complex numbers such that

{\bar{z}}_{1} = i {\bar{z}}_{2}

and

\arg (\frac{z_{1}}{{\bar{z}}_{2}}) = π

, then the argument of

z_{1}

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 26 June 2022 Shift 2>Q 82

If

z^{2} + z + 1 = 0, z \in C

, then

|\sum_{n = 1}^{15} {(z^{s} + (- 1)^{a} \frac{1}{z^{n}})}^{2}|

is equal to _____.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 26 June 2022 Shift 1>Q 83

Let

A = \{z \in C : |\frac{z + 1}{z - 1}| < 1\}

and

B = \{z \in C : \arg (\frac{z - 1}{z + 1}) = \frac{2 π}{3}\}

. Then

A \cap B

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 27 June 2022 Shift 1>Q 84

The area of the polygon, whose vertices are the non-real roots of the equation

\bar{z} = i z^{2}

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 27 June 2022 Shift 2>Q 85

The number of points of intersection

|z - (4 + 3 i) | = 2|

and

|z| + |z - 4| = 6, z \in C

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 28 June 2022 Shift 1>Q 86

The number of elements in the set {

z = a + i b \in ℂ : a, b \in ℤ

and

1 < |z - 3 + 2 i| < 4

} is _____.