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2 years ago

Find the cube roots of 8i. Write the answer in a + bi form.

Mathematics

2 answers:

Murrr4er [49]2 years ago

8 0

Answer:

a0 = ∛8 [ cos [ (pi/2)/3] + i *sin [(pi/2)/3 ] = ∛8 [ cos [ (pi/6)] + i *sin [(pi/6) ] =

2 [ √3/2 + 1/2 * i ] = √3 + 1i

a1 = ∛8 [ cos ( (pi/2)/3 + 2pi/3 ) + i sin ( (pi/2 )/3 + 2pi/3 ) ] =

2 [ cos (5pi/6) + i sin (5pi/6) ] = 2 [ - √3/2 + (1/2)*i ] = - √3 +1i

a2 = ∛8 [ cos ( (pi/2)/3 + 4pi/3 ) + i sin ( (pi/2 )/3 + 4pi/3 ) ] =

2 [ cos(3pi/2) + i sin (3pi/2) ] = 2 [ -1 i ] = -2i

like this

AnnZ [28]2 years ago

3 0

Answer:

It's B

Step-by-step explanation:

Just took the quiz

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Show that each system has no solution<br>y=x+1<br>-x+y=3

Phoenix [80]

Y=x+1
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3 years ago

Factories fully. X to the power of three - x

spayn [35]

The expression x³ - x when factored out is x(x -1)(x + 1)

<h3>How to determine the factored expression?</h3>

From the question, we have the following expression that can be used in our computation:

X to the power of three - x

Express the expression properly

So, we have the following representation

x³ - x

The terms of the above expression are:

x³ and x

And the factor of x³ and x

Factor = x

So, we divide x³ and x by x

The results of these divisions are

x³/x = x²

x/x = 1

So, we have the following results

(x³ - x) = x(x² -1)

Express x² -1 as a difference of two squares

So, we have

(x³ - x) = x(x -1)(x + 1)

Hence, the factored expression is x(x -1)(x + 1)

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11 months ago

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Alecsey [184]

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Step-by-step explanation:

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2 years ago

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A cyclist estimates that he will bike 80 miles this week. He actually bikes 75.5 miles. What is the percent error of the cyclist

maw [93]

Answer:

<em>The percent error of the cyclist's estimate is 5.63%</em>

Step-by-step explanation:

<u>Percentages</u>

The cyclist estimates he will bike 80 miles this week, but he really bikes 75.5 miles.

The error of his estimate in miles can be calculated as the difference between his estimate and the real outcome:

Error = 80 miles - 75.5 miles = 4.5 miles

To calculate the error as a percent, we divide that quantity by the original estimate and multiply by 100%:

Error% = 4.5 / 80 * 100 = 5.625%

Rounding to the nearest hundredth:

The percent error of the cyclist's estimate is 5.63%

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2 years ago

of 320 consumers polled, some purchase blu-ray movies, some only purchase movies on dvd, and some do both. if 300 people polled

Helga [31]

Answer:

20 people only buy dvds.

Step-by-step explanation:

There are two groups in this problem. One group of people that buys dvds and one that buys blu rays. The total amount of people who buy blu rays is 300, but there's an intersection between the groups and the size of this is 280 people who actually buy both. In order to find out how many people only buy DVDs we first need to figure out how many only buy blu-rays. That is:

people who only buy blu rays = people who buy blu rays - people who buys blu rays and dvds

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We can now calculate the amount of people who only buy dvds and that is:

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3 0

3 years ago