Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 102

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IMPORTANT

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The complex numbers given by $1 - 3 i, 4 + 3 i$ and $3 + i$ represent the vertices of

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Important Questions on Complex Numbers

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 103

If

Re (\frac{z + 2 i}{z + 4}) = 0,

then

z

lies on a circle with centre

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 104

If

Im (\frac{z + 2 i}{z + 2}) = 0

then

z

lies on the curve

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 105

In the argand plane, all the complex numbers satisfying

|z - 4 i| + |z + 4 i| = 10

lie on

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 106

If

z = x + i y

and

a

is a real number such that

|z - a i| = |z + a i|

then locus of

z

is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 107

If

P

represents

z = x + i y

in the argand plane and

{|z - 1|}^{2} + {|z + 1|}^{2} = 4,

then the locus of

P

is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 108

All the roots of the equation

a_{1} z^{3} + a_{2} z^{2} + a_{3} z + a_{4} = 3

, where

|a_{i}| \leq 1

,

i = 1, 2, 3, 4

lie outside the circle with centre origin and radius

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 109

The region of argand diagram defined by

|z - 1| + |z + 1| \leq 4

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 110

The locus of the complex number

z

in an Argand plane satisfying the inequality where

\log_{\frac{1}{2}} (\frac{|z - 1| + 4}{3 |z - 1| - 2}) > 1

[Where, |z - 1| \neq \frac{2}{3}]

is