Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 7

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Let $z, ω z$ and $z + ω z$ represent three vertices of $∆ A B C$ , where $ω$ is cube root unity, then

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Important Questions on Complex Numbers

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 8

Which of the following complex numbers lies along the angle bisectors of the lines
$L_{1} : z = (1 + 3 λ) + i (1 + 4 λ)$

$L_{2} : z = (1 + 3 μ) + i (1 - 4 μ)$

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 9

Let

z

and

ω

are two complex numbers such that

| z | \leq 1, | ω | \leq 1

and

| z + i ω | = | z - i ω | = 2

, then

z

equals:

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 10

P (z)

be a variable point in the Argand plane such that

|z| = minimum \{|z - 1|, |z + 1|\},

then

z + z

will be equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 11

For two complex numbers

z_{1}

and

z_{2} : (a z_{1} + b {\bar{z}}_{1}) (c z_{2} + d {\bar{z}}_{2}) = (c z_{1} + d {\bar{z}}_{1}) (a z_{2} + b {\bar{z}}_{2})

if

(a, b, c, d \in R)

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 12

Which of the following locus of z on the complex plane represents a pair of straight lines?

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 13

If the complex numbers

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

represents vertices of an equilateral triangle such that

|z_{1}| = |z_{2}| = |z_{3}|

, then which of following is correct?

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 14

If

S

be the set of real values of

x

satisfying the inequality

1 - \log_{2} \frac{| x + 1 + 2 i | - 2}{\sqrt{2} - 1} \geq 0

, then

S

contains

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Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 15

If

amp (z_{1} z_{2}) = 0

and

|z_{1}| = |z_{2}| = 1

, then