Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 41

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For all the complex numbers $z_{1}, z_{2}$ satisfying $|z_{1} - 3| = 3$ and $|z_{2} - 3 + 18 i| = 2$ then the minimum value of $|z_{1} - z_{2}|$ is equal to

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Important Questions on Complex Numbers

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 42

The algebraic sum of perpendicular distances from the points

1, α_{1}, α_{2}, α_{3}, α_{4}, α_{5}, α_{6}, α_{7}

, where

α_{i}

for

i = 1, 2, \dots, 7

, are complex

8^{th}

roots of unity, from the line

(3 + 2 i) z + (3 - 2 i) \bar{z} + 5 \sqrt{13} = 0

, is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 43

If

z_{1}, z_{2}, z_{3}, \dots, z_{n}

lies on a circle

|z| = 5

then the value of

|z_{1} + z_{2} + \dots + z_{n}| - 25 |\frac{1}{z_{1}} + \frac{1}{z_{2}} + \dots + \frac{1}{z_{n}}|

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 44

The eccentricity of conic represented by

|z - 2| + |z - 2 + 17 i| = 19

is

e

, then

{(19 e)}^{2}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 1

If

z_{1} = \cos θ + i \sin θ

and

1, z_{1}, z_{1}^{2}, z_{1}^{3}, . . . . . . . ., z_{1}^{n - 1}

are vertices of a regular polygon such that

\frac{l m (z_{1}^{2})}{R e (z_{1})} = \frac{\sqrt{5} - 1}{2}

, then the value of

n

is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 2

If

f (x)

and

g (x)

are two polynomials such that the polynomial

h (x) = x f (x^{3}) + x^{2} g (x^{6})

is divisible by

x^{2} + x + 1

, then

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 3

The complex numbers

z_{1}, z_{2}

and

z_{3}

satisfying

\frac{z_{1} - z_{3}}{z_{2} - z_{3}} = \frac{1 - i \sqrt{3}}{2}

are the vertices of a triangle which is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 4

The area of the triangle whose vertices are represented by the complex numbers

0, z, z e^{i α}, (0 < α < π)

equals

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 5

If

z^{2} + z |z| + {|z|}^{2} = 0

, then the locus of

z

is