Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 22

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If there exist exactly one complex number $z$ satisfying the conditions $|z - k i| \leq \sqrt{3}$ and arg $(z) \leq \frac{π}{6}$ (where $k \in R^{+}$ and $i = \sqrt{- 1}$ ), then the value of $k$ is

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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 23

If

|z - 1| = 1

and

z \neq 0, 2

then the possible value of

\frac{z - 2}{z}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 24

The number of values of

z

satisfying the equations

1 + z + z^{2} + z^{3} + \dots + z^{17} = 0

and

1 + z + z^{2} + \dots + z^{11} = 0

simultaneously is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 25

If

{[\frac{1 + \cos θ + i \sin θ}{\sin θ + i (1 + \cos θ)}]}^{4} = \cos n θ + i \sin n θ

then value of

n

is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 26

The value of

\sum_{n = 1}^{7} {(x^{n} + \frac{1}{x^{n}})}^{2}

is (where

x

is a root of

x^{2} - x + 1 = 0

)

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 27

If the locus of a point

z

lying on

|z - 3| + |z - i| = k

represent an ellipse, then

k

can be

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 28

If one vertex of the triangle having maximum area that can be inscribed in the circle

|z| = 2

is

1 + i \sqrt{3}

, then the other vertex of the triangle can be

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 29

If

z_{1}, z_{2}, \dots, z_{100}

are root of equation

1 + z + z^{2} + \dots + z^{100} = 0

, then the value of

\sum_{r = 1}^{100} \frac{1}{z_{r} - 1}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 31

Value of

{(\frac{3}{2} + \frac{i \sqrt{3}}{2})}^{30}

equals