Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 7

EASY

JEE Advanced

IMPORTANT

Earn 100

For a positive integer $n$ , the expression ${(1 - i)}^{n} {(1 - \frac{1}{i})}^{n}$ equals

50% studentsanswered this correctly

Important Questions on Complex Numbers

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 8

If the number

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

is real and positive, then

n

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 9

The smallest positive integer

n

for which

{(\frac{1 + i}{1 - i})}^{n} = - 1

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 10

The smallest positive number

n

for which

{(1 + i)}^{2 n} = {(1 - i)}^{2 n}

( where

i = \sqrt{- 1}

) is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 11

The complex number

\frac{1 + 2 i}{1 - i}

lies in the

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 12

The value of

\frac{{(1 - i)}^{3}}{1 - i^{3}}

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 13

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

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 14

The value of

Re [\frac{{(1 + i)}^{2}}{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 15

If

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

then

\frac{(1 + b + i a)}{(1 + b - i a)}

is equal to