Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 17

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JEE Advanced

IMPORTANT

Earn 100

The number of complex numbers $z$ such that $|z - 1| = |z + 1| = |z - i|$ equals

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Important Questions on Complex Numbers

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 18

If

α

and

β

are the roots of the equation

x^{2} - x + 1 = 0

, then

α^{2009} + β^{2009}

is equal to

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 19

If

|z - \frac{4}{z}| = 2,

then the maximum value of

|z|

is equal to

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 20

The conjugate of a complex number is

\frac{1}{i - 1} .

Then, that complex number is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 21

If

|z + 4| \leq 3

, then the maximum value of

|z + 1|

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 24

If the cube roots of unity are

1, ω, ω^{2},

then the roots of the equation

(x - 1)^{3} + 8 = 0,

are

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 25

If

z_{1}

and

z_{2}

are two non-zero complex numbers such that

|z_{1} + z_{2}| = |z_{1}| + |z_{2}|,

then

\arg (z_{1}) - \arg (z_{2})

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 26

If

ω = \frac{z}{z - \frac{i}{3}}

and

|ω| = 1,

then

z

lies on

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 27

Let

z

and

ω

be two complex numbers such that

\bar{z} + i \bar{ω} = 0

and

\arg (z ω) = π .

Then,

\arg (z)

equals