EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 5 - Complex Numbers>Assam CEE 2016>Q 8

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If $|z - i| \leq 2$ and $z_{0} = 5 + 3 i$ , then the maximum value of $|i z + z_{0}|$ is

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Important Questions on Complex Numbers

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 5 - Complex Numbers>Assam CEE 2016>Q 9

If the equation

a z^{2} + 2 b z + a = 0

, where

a, b

are complex numbers, has both roots purely real, then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 5 - Complex Numbers>Assam CEE 2016>Q 10

If

z = 1 + i \cot θ, \frac{3 π}{2} < θ < 2 π

then

|- \frac{4 z}{i}|

is equal to

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 5 - Complex Numbers>Assam CEE 2016>Q 11

Let

z_{1}

and

z_{2}

be two complex numbers such that

{\bar{z}}_{1} + i z_{2} = 0

and

\arg (z_{1} {\bar{z}}_{2}) = π

, then

\arg ({\bar{z}}_{2})

is equal to

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 5 - Complex Numbers>Assam CEE 2016>Q 12

If

z^{2} + z + 1 = 0

, then the value of

{(z + \frac{1}{z})}^{2} + {(z^{2} + \frac{1}{z^{2}})}^{2} + {(z^{3} + \frac{1}{z^{3}})}^{2} + \dots + {(z^{21} + \frac{1}{z^{21}})}^{2}

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 5 - Complex Numbers>Assam CEE 2016>Q 13

If

z = x + i y

and

ω = \frac{1 - i z}{z - i}

, then

|ω| = 1

implies that, in the complex plane

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 5 - Complex Numbers>Assam CEE 2016>Q 14

If

ω

is an imaginary cube root of unit, then

{(1 + ω - ω^{2})}^{7}

is equal to

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 5 - Complex Numbers>Assam CEE 2016>Q 15

For the complex numbers

z_{1}, z_{2}

satisfying

|z_{1}| = 12

and

|z_{2} - 3 - 4 i| = 5

, the minimum value of

|z_{1} - z_{2}|

is