Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.3>Q 24

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IMPORTANT

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If $z$ and $w$ are two complex numbers simultaneously satisfying the equations, $z^{3} + w^{5} = 0$ and $z^{2} \cdot ω^{- 4} = 1,$ then

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Important Questions on Complex Numbers

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.3>Q 25

Number of ordered pairs

(z, ω)

of the complex numbers

z

and

ω

, satisfying the system of equations,

z^{3} + (\bar{ω})^{7} = 0

and

z^{5} \cdot ω^{11} = 1

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.3>Q 26

If

1, z_{1}, z_{2}, z_{3}, \dots, z_{n - 1}

is the

n^{th}

root of unity and

w

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

\prod_{r = 1}^{n - 1} (ω - z_{r})

cannot be equal to

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.3>Q 27

If

Z_{r}, r = 1, 2, 3, \dots, 50

are the roots of the equation

\sum_{r = 0}^{50} {(Z)}^{r} = 0

, then the value of

\sum_{r = 1}^{50} \frac{1}{Z_{r} - 1}

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 1

|\frac{z - 1}{z + 1}| = 1

represents

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 2

|z - 4| < |z - 2|,

represents the region given by

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 3

If

2 z_{1} - 3 z_{2} + z_{3} = 0

then

z_{1}, z_{2}, z_{3}

are represented by

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 4

If

z = x + i y

such that

|z + 1| = |z - 1|

and

amp (\frac{z - 1}{z + 1}) = \frac{π}{4}

then

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IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 5

If

z^{8} = (z - 1)^{8},

then the roots of this equation are