Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 1

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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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Important Questions on Complex Numbers

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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 5

If a complex number

z

moves such that

| Re (\bar{z}) | + | Im (z) | = \sqrt{3}

, then the area bounded by all such positions of

z

is

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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 7

Consider two complex numbers

z_{1}

and

z_{2}

such that

|z_{1} + z_{2}| = |z_{1}| - |z_{2}|,

then the complex number

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

will always lie on a

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 8

The sum of the real roots of polynomial

72 - 36 z - 26 z^{2} + 13 z^{3} + 2 z^{4} - z^{5} = 0

will be

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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}