Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 83

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IMPORTANT

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If $α$ and $β$ are the complex cube roots of unity, then $α^{3} + β^{3} + α^{- 2} β^{- 2}$ is equal to

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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>Target Exercises>Q 84

If

ω

is a complex cube root of unity, then

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

(1 - ω^{8} + ω^{16})

is equal to

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 85

If

x = ω - ω^{2} - 2

, then the value of

x^{4} + 3 x^{3} + 2 x^{2} - 11 x - 6

is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 86

If

1, ω

and

ω^{2}

are the three cube roots of unity, then

(1 + ω) (1 + ω^{2}) (1 + ω^{4}) (1 + ω^{8}) \dots

to

2 n

factors is equal to

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 87

If

x = a + b + c, y = a α + b β + c

and

z = a β + b α + c

, where

α

and

β

are complex cube roots of unity, then

x y z

is equal to

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 88

The common roots of the equations

z^{3} + 2 z^{2} + 2 z + 1 = 0

and

z^{1985} + z^{100} + 1 = 0

are

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 89

The values of

{(16)}^{\frac{1}{4}}

are

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 90

If

p, q

and

r

are positive integers and

ω

is an imaginary cube root of unity and

f (x) = x^{3 p} + x^{3 q + 1} + x^{3 r + 2}

, then

f (ω)

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 91

If

1, α, α^{2}, \dots, α^{n - 1}

are the

n, n^{th}

roots of unity, then

\sum_{i = 1}^{n - 1} \frac{1}{2 - α^{i}}

is equal to