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Convert the complex number 3 - 3i into its polar representation. a. 3(cos(60degrees) + isin(60degrees)) b. 3āˆš2(cos(135degrees) + isin(135degrees)) c. āˆš3(cos(225degrees) + isin(225degrees)) d. 3āˆš(cos(315degrees) + isin(315degrees))

Respuesta :

Answer:

The correct option is B. 3āˆš2(cos(135Ā°) + iĀ·sin(135Ā°))

Step-by-step explanation:

The complex number is given as : 3 - 3i

Now, comparing this with the standard for : a + bi

ā‡’ a = 3 and b = -3

Now, r = āˆšaĀ² + bĀ²

ā‡’ r = āˆš18

ā‡’ r = 3āˆš2

[tex]\tan\theta=\frac{b}{a}\\\\\implies\tan\theta=\frac{-3}{3}\\\\ \implies\tan\theta =-1\\\\ \implies\theta=\frac{3\pi}{4}\\\\\implies\theta=135[/tex]

Now, The polar form is represented by :

z = r(cosĪø + iĀ·sinĪø)

ā‡’ z = 3āˆš2(cos 135Ā° + iĀ·sin 135Ā°)

Therefore, the correct option is B. 3āˆš2(cos(135Ā°) + iĀ·sin(135Ā°))

artisticzack25

Answer:

3sqrt(cos(315ā°)+isin(315ā°))

Step-by-step explanation:

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