Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 8

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If $|z_{1} - 1| < 1, |z_{2} - 2| < 2, |z_{3} - 3| < 3,$ then $|z_{1} + z_{2} + z_{3}|$

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Important Questions on Complex Numbers

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 9

Let

O = (0, 0); A = (3, 0); B = (0, - 1)

and

C = (3, 2),

then the minimum value of

|z| + |z - 3| + |z + i| + |z - 3 - 2 i|

occur at

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 10

Given

z

is a complex number with modulus

1 .

Then the equation

{[\frac{(1 + i a)}{(1 - i a)}]}^{4} = z

in

' a'

has

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 11

The real values of the parameter

' a'

for which at least one complex number

z = x + i y

satisfies both the equality

|z - a i| = a + 4

and the inequality

|z - 2| < 1

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 12

The points of intersection of the two curves

|z - 3| = 2

and

|z| = 2

in an argand plane are

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 13

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

|z - 2| = 3

and

|z - 2 - 3 i| = 4

on the complex plane is

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 14

If

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

then the locus of

z

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 15

Points

z_{1}

and

z_{2}

are adjacent vertices of a regular octagon. The vertex

z_{3}

adjacent to

z_{2} (z_{3} \neq z_{1})

is represented by :

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 16

If

p = a + b ω + c ω^{2}; q = b + c ω + a ω^{2}

and

r = c + a ω + b ω^{2}

where

a, b, c \neq 0

and

ω

is the non-real complex cube root of unity, then