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Polar Representation of a Complex Number

Amplitude of ...

Question

Amplitude of $(1 - i \sqrt{3})^{4}$ is (where $i = \sqrt{- 1}$ )

$(1 - i \sqrt{3})^{4}$ का कोणांक है (जहाँ $i = \sqrt{- 1}$ )

A

\frac{π}{3}

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B

\frac{π}{6}

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C

Zero

शून्य

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D

\frac{2 π}{3}

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Solution

The correct option is D $\frac{2 π}{3}$

Solution

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Similar questions

Q. The value of

∣ ∣ ∣ ∣ ∣ \frac{\sqrt{3} + i}{{[1 + \frac{1}{(1 - i)}]}^{2}} ∣ ∣ ∣ ∣ ∣

i = \sqrt{- 1}

∣ ∣ ∣ ∣ ∣ \frac{\sqrt{3} + i}{{[1 + \frac{1}{(1 - i)}]}^{2}} ∣ ∣ ∣ ∣ ∣

का मान है (जहाँ

i = \sqrt{- 1}

)

Q. Argument of the complex number

(\frac{i}{2} - \frac{2}{i})

i = \sqrt{- 1}

)

सम्मिश्र संख्या

(\frac{i}{2} - \frac{2}{i})

के कोणांक का मान है (यहाँ

i = \sqrt{- 1}

Q. The value of i⁴⁷ + i⁶³ + i⁷³ + i⁸¹ + i³⁷, is (where

i = \sqrt{- 1}

)

i⁴⁷ + i⁶³ + i⁷³ + i⁸¹ + i³⁷ का मान है (जहाँ

i = \sqrt{- 1}

Q. The modulus-amplitude form of

\sqrt{3} + i

i = \sqrt{- 1}

Q. Express the following complex numbers in the standard form a + i b:
(i)

(1 + i) (1 + 2 i)

\frac{3 + 2 i}{- 2 + i}

\frac{1}{(2 + i)^{2}}

\frac{1 - i}{1 + i}

\frac{(2 + i)^{3}}{2 + 3 i}

\frac{(1 + i) (1 + \sqrt{3} i)}{1 - i}

\frac{2 + 3 i}{4 + 5 i}

\frac{(1 - i)^{3}}{1 - i^{3}}

(1 + 2 i)^{- 3}

\frac{3 - 4 i}{(4 - 2 i) (1 + i)}

(\frac{1}{1 - 4 i} - \frac{2}{1 + i}) (\frac{1 - 4 i}{5 + i})

\frac{5 + \sqrt{2} i}{1 - 2 \sqrt{i}}

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