Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 45

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Non-zero complex number $z$ is such that $z + \frac{1}{z}$ is purely real then sum of possible values of $\arg (z)$ is $k$ , then $k$ equals

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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 46

If

z_{1}, z_{2} \in C, z_{1}^{2} + z_{2}^{2} \in R, z_{1} (z_{1}^{2} - 3 z_{2}^{2}) = 2

and

z_{2} (3 z_{1}^{2} - z_{2}^{2}) = 11

, then the value of

z_{1}^{2} + z_{2}^{2}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 47

Let

| z | = 2

and

w = \frac{z + 1}{z - 1}

, where

z

,

w \in C

then

2 | w - 1 | - | w + 1 | + 1

equals

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

If

x = 3 + 4 i

then the value of

204 x - 70 x^{2} + 12 x^{3} - x^{4}

is

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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 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