Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 4

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JEE Advanced

IMPORTANT

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If $z = x + i y$ such that $|z + 1| = |z - 1|$ and $amp (\frac{z - 1}{z + 1}) = \frac{π}{4}$ then

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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>Work Book Exercise 4.4>Q 5

If

z^{8} = (z - 1)^{8},

then the roots of this equation are

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 6

The equation

z \bar{z} + a \bar{z} + \bar{a} z + b = 0, b \in R

represents a circle, if

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 7

If

z = (λ + 3) + i \sqrt{3 - λ^{2}},

where

|λ| < \sqrt{3},

then locus of

z

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 8

If a point

P

denoting the complex number

z

moves on the complex plane such that

|Re (z)| + |lm (z)| = 1,

then the locus of

z

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 9

The figure formed by four points

1 + 0 i, - 1 + 0 i

,

3 + 4 i

and

\frac{25}{- 3 - 4 i}

on the argand plane is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 10

If

i = \sqrt{- 1},

then define a sequence of complex number by

z_{1} = 0, z_{n + 1} = z_{n}^{2} + i

for

n \geq 1

. In the complex plane, how far from the origin is

z_{111}

?

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 11

The complex numbers whose real and imaginary parts are integers and satisfy the relation

z {\bar{z}}^{3} + z^{3} \bar{z} = 350,

forms a rectangle on the argand plane, the length of whose diagonal is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 12

The locus of

z,

for the

\arg z = - \frac{π}{3}

is