Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 55

EASY

JEE Advanced

IMPORTANT

Earn 100

Among the complex number $z$ satisfying condition $|z + 1 - i| \leq 1,$ the number having the least positive argument is

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Important Questions on Complex Numbers

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 57

If the conjugate of

(x + i y) (1 - 2 i)

is

1 + i,

then

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 60

If

2 x = 3 + 5 i

, then the value of

2 x^{3} + 2 x^{2} - 7 x + 72

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 61

If

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

then

\frac{z_{1}}{z_{2}}

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 62

The value of

|\frac{1 + i \sqrt{3}}{{(1 + \frac{1}{i + 1})}^{2}}|

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 63

If

z_{1}

and

z_{2}

are two non-zero complex numbers such that

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

, then

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

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 65

{[\frac{1 + \cos (\frac{θ}{2}) - i \sin (\frac{θ}{2})}{1 + \cos (\frac{θ}{2}) + i \sin (\frac{θ}{2})}]}^{4 n}

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 66

If

x = \frac{- 3 + i \sqrt{3}}{2}

is a complex number, then the value of

{(x^{2} + 3 x)}^{2} (x^{2} + 3 x + 1)

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 67

If

{(x + i y)}^{\frac{1}{3}} = 2 + 3 i

, then

3 x + 2 y

is equal to