Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 35

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The sum of principal arguments of complex numbers $1 + i, - 1 + i \sqrt{3}, - \sqrt{3} - i, \sqrt{3} - i, i, - 3 i, 2, - 1$ 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 36

If

z_{1}, z_{2}

and

z_{3}, z_{4}

are two pairs of conjugate complex numbers, then

\arg (\frac{z_{1}}{z_{3}}) + \arg (\frac{z_{2}}{z_{4}})

is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 37

If

\arg z = \frac{π}{4}

, then

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 38

The argument of

- 2 + 2 \sqrt{3} i

is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 39

The polar form of complex number

\sqrt{3} + i

is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 40

The amplitude of

\frac{1}{i}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 41

If

z = \frac{1 + 3 i}{1 - i}

, then (where

i = \sqrt{- 1}

)

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 42

The argument of

- 3 i \cdot | 5 - 13 i |

is

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 43

Let

z = 3 + x i

where

x

is a non-zero real number and

i = \sqrt{- 1}

. If the imaginary part of

z^{2}

is equal to imaginary part of

z^{3}

then

x^{2}

is equal to