EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 12th April 2019 Shift 1>Q 58

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IMPORTANT

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The equation $| z - i | = | z - 1 |, i = \sqrt{- 1},$ represents:

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Important Questions on Complex Numbers

HARD

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 12th April 2019 Shift 2>Q 59

Let

z \in C

with

I m (z) = 10

and it satisfies

\frac{2 z - n}{2 z + n} = 2 i - 1

for some natural number

n .

Then

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 12th January 2019 Shift 1>Q 60

If

\frac{z - α}{z + α} (α \in R)

is a purely imaginary number and

|z| = 2

, then a value of

α

is :

MEDIUM

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 12th January 2019 Shift 2>Q 61

Let

z_{1}

and

z_{2}

be two complex numbers satisfying

| z_{1} | = 9

and

| z_{2} - 3 - 4 i | = 4

. Then the minimum value of

|z_{1} - z_{2}|

is :

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 8th April 2018>Q 62

If

α, β \in C

are the distinct roots of the equation

x^{2} - x + 1 = 0,

then

α^{101} + β^{107}

is equal to

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 15th April 2018>Q 63

The set of all

α \in R

, for which

w = \frac{1 + (1 - 8 α) z}{1 - z}

is a purely imaginary number, for all

z \in C

satisfying

|z| = 1

and

R e (z) \neq 1

, is :

EASY

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IMPORTANT

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

The least positive integer

n

for which

{(\frac{1 + i \sqrt{3}}{1 - i \sqrt{3}})}^{n} = 1

is

MEDIUM

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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

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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: