Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 16

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The multiplicative inverse of $(3 + \sqrt{5} i)^{2}$ 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 17

If

z = 3 + i + 9 i^{2} - 6 i^{3}

, then

(\bar{z^{- 1}})

is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 18

The value of

(1 + i) (1 - i^{2}) (1 + i^{4}) (1 - i^{5})

is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 19

If

z = 4 - 9 i

, then

z \bar{z}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 20

The modulus of

\bar{6 + i^{3}} + \bar{9 - i} + \bar{9 + i^{2}}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 21

\frac{3 + 2 i \sin θ}{1 - 2 i \sin θ}

will be purely imaginary, then

\sin^{2} θ

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 22

If

x + i y = \frac{3}{2 + \cos θ + i \sin θ}

, then the value of

x^{2} + y^{2}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 23

The modulus of

i^{25} + (i + 2)^{3}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 24

For any complex number

z

, the minimum value of

| z | + | z - 3 i |

is