Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 47

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JEE Advanced

IMPORTANT

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In the argand plane, the distinct roots of $1 + z + z^{3} + z^{4} = 0 (z$ is a complex number $)$ represent vertices of

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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>Entrances Gallery>Q 48

If

z_{1} = 2 \sqrt{2} (1 + i)

and

z_{2} = 1 + i \sqrt{3},

then

z_{1}^{2} z_{2}^{3}

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 49

The value of

{(1 + i)}^{3} + {(1 - i)}^{3}

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 50

If

z {(2 - i 2 \sqrt{3})}^{2} = i (\sqrt{3} + i)^{4}

, then the amplitude of

z

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 51

If

z_{1}, z_{2}

and

z_{3}

are complex numbers such that

|z_{1}| = |z_{2}| = |z_{3}| = |\frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}}| = 1

, then

|z_{1} + z_{2} + z_{3}|

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 52

If

{(\sqrt{3} i + 1)}^{100} = 2^{99} (a + i b),

then

a^{2} + b^{2}

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 53

The value of

{(1 + \sqrt{3} i)}^{4} + {(1 - \sqrt{3} i)}^{4}

is

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IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 54

If the fourth roots of unity are

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

and

z_{4},

then

z_{1}^{2} + z_{2}^{2} + z_{3}^{2} + z_{4}^{2}

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 55

Among the complex number

z

satisfying condition

|z + 1 - i| \leq 1,

the number having the least positive argument is