EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 5 - Complex Numbers>Assam CEE 2017>Q 5

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The maximum value of $|z|$ when $z$ satisfies the condition $|z - \frac{2}{z}| = 2$ 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 2017>Q 6

If

a, b, c, p, q, r

are six complex numbers, such that

\frac{p}{a} + \frac{q}{b} + \frac{r}{c} = 1 + i

and

\frac{a}{p} + \frac{b}{q} + \frac{c}{r} = 0,

where

i = \sqrt{- 1},

then the value of

\frac{p^{2}}{a^{2}} + \frac{q^{2}}{b^{2}} + \frac{r^{2}}{c^{2}}

is:

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 5 - Complex Numbers>Assam CEE 2017>Q 7

The solutions of the equation

z \bar{(z - 3 i)} = 2 (2 + 3 i)

are:

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

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

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

EASY

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IMPORTANT

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}

EASY

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IMPORTANT

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