Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 50

EASY

NDA & NA EE

IMPORTANT

Earn 100

What is the modulus of $\frac{\sqrt{2} + i}{\sqrt{2} - i}$ , where $i = \sqrt{- 1}$ ?

50% studentsanswered this correctly

Important Questions on Complex Numbers

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 51

Consider the following statements

$I .$ ${(ω^{10} + 1)}^{7} + ω = 0$

$II .$ ${(ω^{105} + 1)}^{10} = p^{10}$ for some prime number $p$ , where, $ω \neq 1$ is a cubic root of unity

Which of the above statement(s) is / are correct?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 52

The value of the sum

\sum_{n = 1}^{13} (i^{n} + i^{n + 1})

, where

i = \sqrt{- 1}

is

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 53

What is the value of

\sqrt{- i}

, where

i = \sqrt{- 1}

?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 54

What is the argument of the complex number

(- 1 - i)

, where

i = \sqrt{- 1}

?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 55

What is one of the square roots of

3 + 4 i

, where

i = \sqrt{- 1}

?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 56

What is the argument of the complex number

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

, where

i = \sqrt{- 1}

?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 57

If

P

and

Q

are two complex numbers, then the modulus of the quotient of

P

and

Q

is

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 58

Let

z = x + i y,

where

x, y

are real variables and

i = \sqrt{- 1}

. If

| 2 z - 1 | = | z - 2 |

, then the point

z

describes