Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.1>Q 10

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The diagram shows several numbers in the complex plane. The circle is the unit circle centered at the origin. One of these numbers is the reciprocal of $F$ , which is

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Important Questions on Complex Numbers

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.1>Q 11

Identify the incorrect statement.

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.1>Q 12

If

z = (3 + 7 i) (p + i q),

where

p, q \in I - \{0\}

is purely imaginary, then minimum value of

{|z|}^{2}

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.1>Q 13

Consider two complex numbers

α

and

β

as

α = {(\frac{a + b i}{a - b i})}^{2} + {(\frac{a - b i}{a + b i})}^{2},

where

a, b \in R

and

β = \frac{z - 1}{z + 1},

where

|z| = 1,

then

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.1>Q 14

If

z

is a complex number having the argument

θ

,

0 < θ < \frac{π}{2}

and satisfying the equality

|z - 3 i| = 3

, then,

\cot θ - \frac{6}{z}

is equal to

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.2>Q 1

The maximum and minimum values of

|z + 1|

when

|z + 3| \leq 3

are

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.2>Q 2

The region represented by inequalities

\arg z \leq \frac{π}{3}, |z| \leq 2, Im (z) \geq 1

in the argand diagram is given by

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.2>Q 3

If

\frac{1 + 2 i}{2 + i} = r (\cos θ + i \sin θ),

then

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.2>Q 4

If

z_{1}

and

z_{2}

are two non-zero complex numbers, such that

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

, then

\arg (z_{1}) - \arg (z_{2})

is equal to