Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 24

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If the complex number $z$ satisfies the condition $|z| \geq 3,$ then the least value of $|z + \frac{1}{z}|$ is equal to

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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 25

z_{1} = \frac{a}{1 - i}, z_{2} = \frac{b}{2 + i}, z_{3} = a - b i,

for

a, b \in R

and

z_{1} - z_{2} = 1,

then the centroid of the triangle formed by the points

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

in the argand plane is given by

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 26

Let

λ \in R

. If the origin and the non-real roots of

2 z^{2} + 2 z + λ = 0

form three vertices of an equilateral triangle in the argand plane, then

λ

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 27

If

a, b, c

and

u, v, w

are complex numbers representing the vertices of two triangles, such that

c = (1 - r) a + r b

and

w = (1 - r) u + r v .

When

r

is a complex number, then the two triangles

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 28

On the complex plane,

Δ O A P

and

Δ O Q R

are similar and

l (O A) = 1

. If the points

P

and

Q

denote the complex numbers

z_{1}

and

z_{2}

, then the complex numbers

z

denoted by the point

R

is given by
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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 29

Intercept made by the circle

z \bar{z} + \bar{α} z + α \bar{z} + r = 0

on the real axis on complex 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 30

The equation of the radical axis of the two circles represented by the equations,

|z - 2| = 3

and

|z - 2 - 3 i| = 4

on the complex plane is

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

The value of

\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} - 1

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 2

i^{57} + \frac{1}{i^{125}},

when simplified has the value