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

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JEE Advanced

IMPORTANT

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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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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 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

HARD

JEE Advanced

IMPORTANT

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

IMPORTANT

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

HARD

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

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 111

The closest distance of the origin from a curve given as

a \bar{z} + \bar{a} z + a \bar{a} = 0

(

a

is a complex number), 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 112

Let

a

be a complex number such that

|a| < 1

and

z_{1}, z_{2}, \dots, z_{n}

be the vertices of a polygon such that

z_{k} = 1 + a + a^{2} + \dots a^{k}

, then the vertices of the polygon lie within the circle

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 113

If

z_{1}, z_{2}, z_{3}

and

z_{4}

are the four complex numbers represented by the vertices of a quadrilateral taken in order such that

z_{1} - z_{4} = z_{2} - z_{3}

and

amp (\frac{z_{4} - z_{1}}{z_{2} - z_{1}}) = \frac{π}{2}

, then the quadrilateral is a

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 114

The locus of

z

satisfying

Im (z^{2}) = 4

is