EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Complex Numbers>CG PET 2019>Q 8

EASY

CG PET

IMPORTANT

Earn 100

If $ω$ is a non-real cube root of unity, then the expression $(1 - ω) (1 - ω^{2}) (1 + ω^{4}) (1 + ω^{8})$ is equal to

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Important Questions on Complex Numbers

HARD

CG PET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Complex Numbers>CG PET 2017>Q 1

If

x = 9^{1 / 3} 9^{1 / 9} 9^{1 / 27} ... \infty

$y = 4^{1 / 3} 4^{- 1 / 9} 4^{1 / 27} ... \infty$

$z = \sum_{r = 1}^{\infty} {(1 + i)}^{- r}$ ,

then $\arg (x + y z)$ will be

MEDIUM

CG PET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Complex Numbers>CG PET 2017>Q 2

If

z = x + i y

is a complex number where

x

and

y

are integers. Then, the area of the rectangle whose vertices are the roots of the equation

z {\bar{z}}^{3} + \bar{z} z^{3} = 350

, is

MEDIUM

CG PET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Complex Numbers>CG PET 2018>Q 3

If

e^{i θ} = \cos θ + i \sin θ

, the the value of

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

is

MEDIUM

CG PET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Complex Numbers>CG PET 2019>Q 4

The value of

{(1 + i)}^{8} + {(1 - i)}^{8}

is

EASY

CG PET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Complex Numbers>CG PET 2019>Q 5

If

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

and

\arg (z_{1}) + \arg (z_{2}) = 0

, then

EASY

CG PET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Complex Numbers>CG PET 2019>Q 6

If

z

is a point on the argand plane such that

|z - 1| = 1,

then

\frac{z - 2}{z}

is equal to

MEDIUM

CG PET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Complex Numbers>CG PET 2018>Q 7

If for complex numbers

z_{1}

and

z_{2}

, arg

(\frac{z_{1}}{z_{2}}) = 0

, then

|z_{1} - z_{2}|

is equal to

EASY

CG PET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Complex Numbers>CG PET 2019>Q 8

If

ω

is a non-real cube root of unity, then the expression

(1 - ω) (1 - ω^{2}) (1 + ω^{4}) (1 + ω^{8})

is equal to