Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 48

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If $x = 3 + 4 i$ then the value of $204 x - 70 x^{2} + 12 x^{3} - x^{4}$ 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 1

Consider three complex numbers

z_{1}, z_{2}, z_{3}

such that

|z_{1}| = 1, |z_{2}| = 2, |z_{3}| = 3 .

The value of

|\frac{36 z_{1} + 9 z_{2} + 4 z_{3}}{\frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}}}|

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 2

If

Im (z) = 2

and

z_{1} = 1 + i,

then the minimum value of

|z - z_{1}|

is (where

i = \sqrt{- 1}

)

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 3

If

α, β, γ

are three distinct non-zero complex numbers such that

|β| = \frac{1}{| γ |},

then the value of

|\frac{β γ - α}{1 - \bar{α} β γ}|

will be

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 4

The argument of complex number

' z'

satisfying the equation

z + \bar{z} = 6

, can not be

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 6

If both the roots of the quadratic equation

a x^{2} + b x + c = 0; a, b, c \in R - {0}

are nonreal and if '

θ

' denotes the principle argument of the complex number

Z = a + i c,

then which of the following options is necessarily true?

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 9

If

f (x) = 7 x^{5} + 3 x^{4} + a_{1} x^{3} + a_{2} x^{2} + a_{3} x + 1

such that for any

z = x + i y

where

x y \neq 0

and

x, y \in R, f (\bar{z}) = \bar{f (z)}

then the product of

a_{1} a_{2} a_{3}

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 3

If

| z + ω |^{2} = | z |^{2} + | ω |^{2}

, where

z

and

ω

are complex numbers, then

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 7

If

z_{1}, z_{2}

be two complex numbers satisfying the equation

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

, then