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3 years ago

Plssss help high school mathematics . Last option is

Mathematics

1 answer:

nordsb [41]3 years ago

7 0

Answer:

it would be A but i'm not 100% sure brainliest pls

Step-by-step explanation:

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Which of the following is a third root of the given complex number.

Leokris [45]

Answer:

The correct option is C.

Step-by-step explanation:

The given complex number is

$z=64(\cos[\frac{\pi}{7}]-i\sin[\frac{\pi}{7}])$

We need to find the third root of the given complex number.

$z^{\frac{1}{3}}=(64(\cos[\frac{\pi}{7}]-i\sin[\frac{\pi}{7}]))^{\frac{1}{3}}$

$z^{\frac{1}{3}}=64^{\frac{1}{3}}(\cos[\frac{\pi}{7}]-i\sin[\frac{\pi}{7}])^{\frac{1}{3}}$

$z^{\frac{1}{3}}=4(\cos[\frac{\pi}{7}]-i\sin[\frac{\pi}{7}])^{\frac{1}{3}}$

De moivre's theorem:

$(\cos\theta+i\sin\theta)^n=\cos n\theta+i\sin n\theta$

where, n is an integer.

Using de moivre's theorem, we get

$z^{\frac{1}{3}}=4(\cos[\frac{\pi}{7}\times \frac{1}{3}]-i\sin[\frac{\pi}{7}\times \frac{1}{3}])$

$z^{\frac{1}{3}}=4(\cos[\frac{\pi}{21}]-i\sin[\frac{\pi}{21}])$

Therefore the correct option is C.

6 0

3 years ago

Read 2 more answers

After finding the third angle of a right triangle if the measure of one of the angles is 25°, prove how you know the measure of

Lelechka [254]

The answer is C so do that one

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2 years ago

What is 10√94 simplified. Its not 98 or its decimal form.

slavikrds [6]

Answer:

Step-by-step explanation:

i think 96(probably)

have a nice day

3 0

3 years ago

Julie Myrick has a credit card that has an APR of 15%, applied at a daily

Fed [463]

Answer. 332.78

Step-by-step explanation:

I subtracted and as awesome its right trust me.

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3 years ago

I need this pleaseeeee!!!!

fiasKO [112]

Answer:

the answer is 0004..................

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3 years ago