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

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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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Important Questions on Complex Numbers

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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

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 32

Let

z_{1} = 5 + i

and

z_{2} = 2 - 4 i

(where

i = \sqrt{- 1}

). Let

z

be a complex number such that

\arg (\frac{z - z_{1}}{z_{2} - z}) = \frac{π}{2}

, then

z

satisfies

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 33

If

z

and

\bar{z}

represent adjacent vertices of a regular polygon of

λ

sides whose centre is at origin and if

\frac{l m (z)}{Re (z)} = \sqrt{2} - 1

, then

λ

equals

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 34

If

1, ω, ω^{2}, . . ., ω^{n - 1}

are the

n, n^{th}

roots of unity, the value of

(7 - ω) (7 - ω^{2}) . . . (7 - ω^{n - 1})

equals

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 35

Let

u

and

v

are two complex such that

|u| \neq |v|

and

|u| = 1

and

z = \frac{a u + b}{u - v}

, where

z = x + i y

and

a, b

are fixed complex numbers then the locus of

z

is

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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