Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.2>Q 10

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JEE Advanced

IMPORTANT

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All real numbers $x,$ which satisfy the inequality $|1 + 4 i - 2^{- x}| \leq 5,$ where $i = \sqrt{- 1}, x \in R$ are

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Important Questions on Complex Numbers

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.2>Q 11

Square root of

x^{2} + \frac{1}{x^{2}} - \frac{4}{i} (x - \frac{1}{x}) - 6

, where

x \in R

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.2>Q 12

The minimum value of

|1 + z| + |1 - z|

, where

z

is a complex number, is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.2>Q 13

If

\arg (z + a) = \frac{π}{6}

and

\arg (z - a) = \frac{2 π}{3}, a \in R^{+},

then

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.2>Q 14

Let

z

be a complex number satisfying the equation

{(z^{3} + 3)}^{2} = - 16

, then

|z|

has the value equal to

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.2>Q 15

For

z_{1} = \sqrt[6]{\frac{1 - i}{1 + i \sqrt{3}}}, z_{2} = \sqrt[6]{\frac{1 - i}{\sqrt{3} + i}}, z_{3} = \sqrt[6]{\frac{1 + i}{\sqrt{3} - i}}

which of the following holds good?

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.3>Q 1

If

ω

is a non-real cube root of unity, then the expression

(1 - ω) (1 - ω^{2}) (1 + ω^{4}) (1 + ω^{8})

is equal to

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.3>Q 2

x^{3 m} + x^{3 n - 1} + x^{3 r - 2},

where

m, n, r \in N

is divisible by

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.3>Q 3

If $ω$ is a non-real cube root of unity, then $\frac{1 + 2 ω + 3 ω^{2}}{2 + 3 ω + ω^{2}} + \frac{2 + 3 ω + ω^{2}}{3 + ω + 2 ω^{2}}$ is equal to