Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 55

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Let principle argument of a complex number be re-defined between $(π, 3 π],$ then sum of principle arguments of roots of equation $z^{6} + z^{3} + 1 = 0$ is

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Important Questions on Complex Numbers

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 56

If

|z| = 1

and

ω = \frac{z - 1}{z + 1},

where

z \neq - 1,

then

R e (ω)

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 58

If

(2 + i) (2 + 2 i) (2 + 3 i) \dots \dots (2 + n i) = x + i y,

then the value of

5.8.13 \dots \dots . . (4 + n^{2})

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 59

If

z = x + i y

satisfies

amp (z - 1) = amp (z + 3)

, then the value of

(x - 1) : y

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 60

If

z_{1} = - 3 + 5 i; z_{2} = - 5 - 3 i

and

z

is a complex number lying on the line segment joining

z_{1} & z_{2},

then

a r g (z)

can be

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 61

If

(1 + i) z = (1 - i) \bar{z}

, then

z

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 62

Let

z

and

ω

be two non-zero complex numbers such that

|z| = |ω|

and

a r g z = π - a r g ω,

then

z

equals

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 63

If

z_{1}

and

z_{2}

are two non-zero complex numbers such that

|\frac{z_{1}}{z_{2}}| = 2

and

\arg (z_{1} z_{2}) = \frac{3 π}{2},

then

\frac{{\bar{z}}_{1}}{z_{2}}

is equal to -

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Alpha Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>Exercise-1>Q 64

Number of complex numbers

z

such that

|z| = 1

and

|\frac{z}{\bar{z}} + \frac{\bar{z}}{z}| = 1

is

(a r g (z) \in |0, 2 π|)