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3 years ago

both brian and jermaine solve the problem. brian says the answer is $40,704. jermaine's answer is $4,604.

1 answer:

Studentka2010 [4]3 years ago

7 0

Could you possibly be more specific?what math problem did they solve? i can help but just be a little more specific so i can answer your question

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Which expression is a fourth root of -1+isqrt3?

aleksklad [387]

Answer:

Step-by-step explanation:

$\sf n^{th}$ roots of a complex number is given by DeMoivre's formula.

$\sf \boxed{\bf r^{\frac{1}{n}}\left[Cos \dfrac{\theta + 2\pi k}{n}+i \ Sin \ \dfrac{\theta+2\pi k}{n}\right]}$

Here, k lies between 0 and (n -1) ; n is the exponent.

$\sf -1 + i\sqrt{3}$

a = -1 and b = √3

$\sf \boxed{r=\sqrt{a^2+b^2}} \ and \ \boxed{\theta = Tan^{-1} \ \dfrac{b}{a}}$

$\sf r = \sqrt{(-1)^2 + 3^2}\\\\ = \sqrt{1+9}\\\\=\sqrt{10}$

$\sf \theta = tan^{-1} \ \dfrac{\sqrt{3}}{-1}\\\\ = tan^{-1} \ (-\sqrt{3})$

$\sf = \dfrac{-\pi }{3}$

n = 4

For k = 0,

$\sf z = \sqrt[4]{10}\left[Cos \ \dfrac{\dfrac{-\pi}{3} +0}{4}+iSin \ \dfrac{\dfrac{-\pi}{3}+0}{4}\right] \\\\\\z= \sqrt[4]{10} \left[Cos \ \dfrac{ -\pi }{12}+iSin \ \dfrac{-\pi}{12}\right]\\\\\\z = \sqrt[4]{10}\left[-Cos \ \dfrac{\pi}{12}-i \ Sin \ \dfrac{\pi}{12}\right]$

For k =1,

$\sf z = \sqrt[4]{10}\left[Cos \ \dfrac{5\pi}{12}+i \ Sin \ \dfrac{5\pi}{12}\right]$

For k =2,

$z = \sqrt[4]{10}\left[Cos \ \dfrac{11\pi}{12}+i \ Sin \ \dfrac{11\pi}{12}\right]$

For k = 3,

$\sf z = \sqrt[4]{10}\left[Cos \ \dfrac{17\pi}{12}+i \ Sin \ \dfrac{17\pi}{12}\right]$

For k = 4,

$\sf z =\sqrt[4]{10}\left[Cos \ \dfrac{23\pi}{12}+i \ Sin \ \dfrac{23\pi}{12}\right]$

4 0

1 year ago

elaina wrote two correct variable expressions to represent the phrase “one-fourth of a number.” which variable expressions could

antiseptic1488 [7]

One-fourth of a number

1/4n and n/4

5 0

3 years ago

Read 2 more answers

The population of an island is 6000 people this year and is projected to be 6300 people next year, by what percentage is the pop

Julli [10]

Answer:

5% increase

Step-by-step explanation:

First, find how much it increased:

6300 - 6000

= 300

Then, to find the percent increase, divide 300 by 6000

300/6000

= 0.05

So, there was a 5% increase in the population

8 0

3 years ago

What percent of 150 is 162

Novay_Z [31]

To find a percentage of a number, you divide by that number.
So to find what percent of 150 162 is, you divide 162 by 150
162 ÷ 150 = 1.08
Now, to find the percentage, we take the decimal and move the point two places to the right.
1.08 = 108%
162 is 108% of 150.

5 0

2 years ago

One kitty weighs 2 pounds 4 ounces. Another kitten weighs 2 ounces less. What is the combined weight of the two kittens in ounce

My name is Ann [436]

70 ounces because there are 16 ounces in a pound so 16 x2 equals 32 + 2ounces equals 36 - 2 equals 34 , 34 + 36 = 70 ounces in total .

3 0

3 years ago