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

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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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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 4.4>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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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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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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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

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 13

If

z_{1}

and

z_{2}

are two complex numbers and

\arg \frac{z_{1} + z_{2}}{z_{1} - z_{2}} = \frac{π}{2}

but

|z_{1} + z_{2}| \neq |z_{1} - z_{2}|,

then the figure formed by the points represented by

0, z_{1}

,

z_{2}

and

z_{1} + z_{2}

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 14

z_{1}

and

z_{2}

are two distinct points in an argand plane. If

a |z_{1}| = b |z_{2}|,

where

a, b \in R,

then the point

\frac{a z_{1}}{b z_{2}} + \frac{b z_{2}}{a z_{1}}

is a point on the

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IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 16

If

z_{1}^{2} + z_{2}^{2} + 2 z_{1} z_{2} \cos θ = 0,

then the points represents by

z_{1}, z_{2}

and the origin form

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 17

Complex numbers

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

are the vertices

A, B

and

C

, respectively of an isosceles right angled triangle, right angled at

C

. Then,

{(z_{1} - z_{2})}^{2}

is equal to