Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-3>Q 24

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If $z$ a complex number such that $|z| \geq 2$ , then the minimum value of $|z + \frac{1}{2}|$

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Important Questions on Complex Numbers

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-3>Q 25

A complex number

z

is said to be unimodular, if

|z| = 1

Suppose

z_{1}

and

z_{2}

are complex numbers such that

\frac{z_{1} - 2 z_{2}}{2 - z_{1} {\bar{z}}_{2}}

is unimodular and

z_{2}

is not unimodular. Then, the point

z_{1}

lies on a

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-3>Q 26

A value of

θ

for which

\frac{2 + 3 isinθ}{1 - 2 isinθ}

is purely imaginary, is

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-3>Q 27

If

α, β \in C

are the distinct roots of the equation

x^{2} - x + 1 = 0,

then

α^{101} + β^{107}

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-3>Q 28

Let

α

and

β

be two roots of the equation

x^{2} + 2 x + 2 = 0

, then

α^{15} + β^{15}

is equal to :

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-3>Q 29

Let

z

be a complex number such that

| z | + z = 3 + i

(where

i = \sqrt{- 1}

).Then,

| z |

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-3>Q 30

Let

z_{1}

and

z_{2}

be two complex numbers satisfying

| z_{1} | = 9

and

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

. Then the minimum value of

|z_{1} - z_{2}|

is :

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-4>Q 2

If

|z_{1}| = 2, |z_{2}| = 3, |z_{3}| = 4

and

|2 z_{1} + 3 z_{2} + 4 z_{3}| = 4,

then find the value of

|8 z_{2} z_{3} + 27 z_{3} z_{1} + 64 z_{1} z_{2}|

.

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-4>Q 3

If

{|z|}^{2} + \bar{A} z^{2} + A {\bar{z}}^{2} + B \bar{z} + \bar{B} z + c = 0

represents a pair of intersecting lines with angle of intersection

θ

, then find the value of

|A|

.