Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 53

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If $|\frac{z - α}{z - β}| = k, k > 0$ where, $z = x + i y$ and $α = α_{1} + i α_{2}, β = β_{1} + i β_{2}$ are fixed complex numbers. Then which of the following are true

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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 54

The locus of equation

Arg (\frac{z - 1 - 2 i}{z + 3 + i}) = \frac{π}{3}

represents part of circle in which

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 55

The equation

‖ z + i | - | z - i ‖ = k

represents -

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 56

The equation

| z - i | + | z + i | = k, k > 0,

can represent

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 57

If

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

and

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

are represented by the vertices of an equilateral triangle then

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 58

Let

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

be three distinct complex numbers satisfying,

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

Let

A, B & C

be the points representing vertices of equilateral triangle in the Argand plane corresponding to

z_{1}, z_{2}

and

z_{3},

respectively. Which of the following are true

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 59

If

1, α_{1}, α_{2}, α_{3}, \dots \dots, α_{n - 1}

be the

n^{th}

roots of unity, then which of the following are true

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 60

Which of the following are true.

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 61

If

α, β, γ

are distinct roots of

x^{3} - 3 x^{2} + 3 x + 7 = 0

and

ω

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

\frac{α - 1}{β - 1} + \frac{β - 1}{γ - 1} + \frac{γ - 1}{α - 1}

can be equal to