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

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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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Important Questions on Complex Numbers

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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

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 17

The points

z_{1} = 3 + \sqrt{3} i

and

z_{2} = 2 \sqrt{3} + 6 i

are given on a complex plane. The complex number lying on the bisector of the angle formed by the vectors

z_{1}

and

z_{2}

is :

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 18

Let

ω

be the non real cube root of unity which satisfy the equation

h (x) = 0

where

h (x) = x f (x^{3}) + x^{2} g (x^{3})

If

h (x)

is polynomial with real coefficient then which statement is incorrect.

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-2>Q 19

If

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

be the

n^{th}

roots of unity, then the value of

\sin \frac{π}{n} \cdot \sin \frac{2 π}{n} \cdot \sin \frac{3 π}{n} \dots \dots . . \sin \frac{(n - 1) π}{n}

equals