Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 26

HARD

JEE Advanced

IMPORTANT

Earn 100

If $z = x + i y$ lies in $III$ quadrant, then $\frac{\bar{z}}{z}$ also lies in $III$ quadrant, if

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Important Questions on Complex Numbers

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 27

The conjugate complex number of

\frac{2 - i}{{(1 - 2 i)}^{2}}

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 28

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

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 29

The value of

|\sqrt{2 i} - \sqrt{- 2 i}|

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 30

If

\frac{1 - i x}{1 + i x} = a - i b

and

a^{2} + b^{2} = 1,

where

a

and

b

are real, then

x

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 31

The modulus of

\frac{{(3 + 2 i)}^{2}}{(4 - 3 i)}

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 32

If

x + i y = \frac{u + i v}{u - i v},

then

x^{2} + y^{2}

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 33

If

(1 + i) (1 + 2 i) (1 + 3 i) \dots (1 + n i) = α + i β,

=

then

2 \cdot 5 \cdot 10 \dots (1 + n^{2})

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 34

The principal argument of the complex number

\frac{{(1 + i)}^{5} {(1 + \sqrt{3} i)}^{2}}{- 2 i (- \sqrt{3} + i)}

is