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

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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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Important Questions on Complex Numbers

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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

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

If

|\frac{2 i z_{1} - z_{1} - z_{2}}{2 i z_{1} + z_{1} + z_{2}}| = |\frac{\cos 2 ϕ + i \sin 2 ϕ}{\cos 2 ϕ - i \sin 2 ϕ}|

and

z_{1}, z_{2}

are non-zero complex numbers, then

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

If

z = 4 + 3 \sqrt{20} i, i = \sqrt{- 1},

then the positive value of

(\sqrt{z} + \sqrt{\bar{z}})^{2}

is equal to

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

The roots of the equation

{(x - 1)}^{3} + 8 = 0

are