EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 16th April 2018>Q 64

EASY

JEE Main

IMPORTANT

Earn 100

The least positive integer $n$ for which ${(\frac{1 + i \sqrt{3}}{1 - i \sqrt{3}})}^{n} = 1$ is

50% studentsanswered this correctly

Important Questions on Complex Numbers

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 2nd April 2017>Q 65

Let

ω

be a complex number such that

2 ω + 1 = z

where

z = \sqrt{- 3}

. If

|\begin{matrix} 1 & 1 & 1 \\ 1 & - ω^{2} - 1 & ω^{2} \\ 1 & ω^{2} & ω^{7} \end{matrix}| = 3 k,

Then

k

can be equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 8th April 2017>Q 66

Let

z \in C,

the set of complex numbers. Then the equation,

2 |z + 3 i| - |z - i| = 0

represents:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 9th April 2017>Q 67

The equation

I m (\frac{i z - 2}{z - i}) + 1 = 0, z \in C, z \neq i

represents a part of a circle having radius equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 9th April 2016>Q 68

The point represented by

2 + i

in the Argand plane moves

1

unit eastwards, then

2

units northwards and finally from there

2 \sqrt{2}

units in the south-west wards direction. Then its new position in the Argand plane is at the point represented by :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 3rd April 2016>Q 69

A value of

θ

for which

\frac{2 + 3 i \sin θ}{1 - 2 i \sin θ}

is purely imaginary, is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 10th April 2016>Q 70

Let

z = 1 + a i

, be a complex number,

a > 0

, such that

z^{3}

is a real number. Then, the sum

1 + z + z^{2} + \dots . + z^{11}

is equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 10th April 2015>Q 71

The largest value of

r

, for which the region represented by the set

\{ω \in C| |ω - 4 - i| \leq r\}

is contained in the region represented by the set

\{z \in C| |z - 1| \leq |z + i|\}

, is equal to :

HARD

JEE Main

IMPORTANT

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

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