Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 19

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The number of common solutions of the equations $z^{n} = 1 + i$ and $z^{m} = 2 - i, n, m \in N z \in C$ 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 20

Let

ω = \cos 3 ° + i \sin 3 °

then

\sum_{r = 1}^{10} Re (ω^{2 r - 1})

equals

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 21

If

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

are the roots of equation

z^{3 n + 1} = 1, (n \in N)

and

ω

is an imaginary cube root of unity. Then the value of

|(α_{1} - ω) (α_{2} - ω) (α_{3} - ω) \dots (α_{3 n} - ω)|

is

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

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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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