Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 22

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If $z, z_{1}$ and $z_{2}$ are complex numbers such that $z = z_{1} z_{2}$ and $|{\bar{z}}_{2} - z_{1}| \leq 1$ , then the maximum value of $|z| - Re (z)$ is

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Important Questions on Complex Numbers

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 23

Let

z_{1}, z_{2}

and

z_{3}

be three complex numbers such that

z_{1} + z_{2} + z_{3} = z_{1} z_{2} + z_{2} z_{3} + z_{1} z_{3} = z_{1} z_{2} z_{3} = 1

. Then the area of triangle formed by points

A (z_{1}), B (z_{2})

and

C (z_{3})

in complex plane is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 24

Let

α

be the non-real

5^{th}

root of unity. If

z_{1}

and

z_{2}

are two complex numbers lying on

|z| = 2

, then the value of

\sum_{t = 0}^{4} {| z_{1} + α^{t} z_{2} |}^{2}

is_.

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 25

Let $z_{1}, z_{2}, z_{3} \in C$ such that $|z_{1}| = |z_{2}| = |z_{3}| = |z_{1} + z_{2} + z_{3}| = 4$ . If $|z_{1} - z_{2}| = |z_{1} - z_{3}|$ and $z_{1} \neq z_{3}$ , then the value of $|z_{1} + z_{2}| . |z_{1} + z_{3}|$ is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 26

Let the points

A (z_{1})

and

B (z_{2})

be points lying on the curve

|z - 3 - 4 i| = 5

, where

|z_{1}|

is maximum. Now,

A (z_{1})

is rotated about the origin in an anticlockwise direction through an angle of

90 °

, reaching

P (z_{0})

. If points

A

,

B

and

P

are collinear, then the value of

(|z_{0} - z_{1}| . |z_{0} - z_{2}|)

is:

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 27

If

z_{1}, z_{2}

and

z_{3}

are three points lying on the circle

|z| = 2

, then minimum of

{|z_{1} + z_{2}|}^{2} + {|z_{2} + z_{3}|}^{2} + {|z_{3} + z_{1}|}^{2}

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 28

Minimum value of

|z_{1} + 1| + |z_{2} + 1| + |z_{1} z_{2} + 1|

. If

|z_{1}| = 1

and

|z_{2}| = 1

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 29

If

|z_{1}| = 2

and

(1 - i) z_{2} + (1 + i) {\bar{z}}_{2} = 8 \sqrt{2}

, then the minimum value of

|z_{1} - z_{2}|

is _____ units.

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 30

Given that

1 + 2 {|z|}^{2} = {|z^{2} + 1|}^{2} + 2 {|z + 1|}^{2}

, then the value of

|z (z + 1)|

is_.