Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 16

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The complex number $z_{1}, z_{2}$ satisfies the equation $z + 1 + 8 i = |z| (1 + i)$ , where $i = \sqrt{- 1}$ then the equation whose roots are $|z_{1}|$ and $|z_{2}|$ 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 18

If

f (n, θ) = \sum_{r = 0}^{n} \frac{\cos (r θ)}{2^{r}}

, then the value of

\lim_{n \to \infty} f (n, \frac{π}{3})

is equal to

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

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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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 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 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 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 36

If '

α

' denotes

2020^{th}

root of unity then

1 + 2 α + 3 α^{2} + . . .

upto

2020

terms is equal to