EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 4th April 2015>Q 72

HARD

JEE Main

IMPORTANT

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A complex number $z$ is said to be unimodular if $|z| = 1$ . Let $z_{1}$ and $z_{2}$ are complex numbers such that $\frac{z_{1} - 2 z_{2}}{2 - z_{1} z_{2}}$ is unimodular and $z_{2}$ is not unimodular, then the point $z_{1}$ lies on a

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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 - 11th April 2015>Q 73

If

z

is a non-real complex number, then the minimum value of

\frac{I m z^{5}}{{(I m z)}^{5}}

is (Where

I m z =

Imaginary part of

z

)

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 19th April 2014>Q 74

For all complex numbers

z

of the form

1 + i α, α \in R,

if

z^{2} = x + i y,

then

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 9th April 2014>Q 75

Let

w (I m w \neq0)

be a complex number. Then, the set of all complex numbers

z

satisfying the equation

w - \bar{w} z = k (1 - z)

, for some real number

k

, is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 6th April 2014>Q 76

If

z

is a complex number such that

|z| \geq 2,

then the minimum value of

|z + \frac{1}{2}|

:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 7th April 2013>Q 77

If

z

is a complex number of unit modulus and argument

θ

, then arg

(\frac{1 + z}{1 + \bar{z}})

can be equal to

(given z \neq - 1)

MEDIUM

JEE Main

IMPORTANT

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

Let

A = \{z \in C : 1 ⩽ |z - (1 + i)| ⩽ 2\}

and

B = \{z \in A : |z - (1 - i)| = 1\}

. Then,

B

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