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Dominik [7]
3 years ago
15

De moirve's (√3-i ÷ √3+i)^6 = 1

Mathematics
1 answer:
bulgar [2K]3 years ago
7 0

(√3 - <em>i </em>) / (√3 + <em>i</em> ) × (√3 - <em>i</em> ) / (√3 - <em>i</em> ) = (√3 - <em>i</em> )² / ((√3)² - <em>i</em> ²)

… = ((√3)² - 2√3 <em>i</em> + <em>i</em> ²) / (3 - <em>i</em> ²)

… = (3 - 2√3 <em>i</em> - 1) / (3 - (-1))

… = (2 - 2√3 <em>i</em> ) / 4

… = 1/2 - √3/2 <em>i</em>

… = √((1/2)² + (-√3/2)²) exp(<em>i</em> arctan((-√3/2)/(1/2))

… = exp(<em>i</em> arctan(-√3))

… = exp(-<em>i</em> arctan(√3))

… = exp(-<em>iπ</em>/3)

By DeMoivre's theorem,

[(√3 - <em>i </em>) / (√3 + <em>i</em> )]⁶ = exp(-6<em>iπ</em>/3) = exp(-2<em>iπ</em>) = 1

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I’m stuck I need help
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Answer:

X=6

Step-by-step explanation:

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Simplify;x=12/2=6

8 0
3 years ago
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She is incorrect because 14 multiplied by 2 equals 28, which means she wouldn’t have any money left over.
5 0
2 years ago
A study was done that looked at how much red meat people consumed and how long they lived. The correlation r was found to be 0.9
AVprozaik [17]

Answer:

False

Step-by-step explanation:

Since the correlation r was found to be 0.98 (a value closer to 1).  

Let X =how much red meat people consumed

let Y = how long they lived.

where the x-values are the values of the deviations of co-ordinates X from Xₙ, their mean value and the y-values are the values of the deviations of co-ordinates Y from Yₙ, their mean value.

That is, x=(X−Xₙ) and y=(Y−Yₙ).

The results of this determination give values of r lying between +1 and −1, where;

+1 indicates perfect direct  correlation,

−1 indicates perfect inverse correlation and

0 indicates that no correlation exists.

Between these values, the smaller the value of r, the less is the amount of correlation which exists.

Generally, values of r in the ranges 0.7 to 1 and −0.7 to −1 show that a fair amount of correlation exists.

therefore, it can be seen that there is a perfect relationship between the quantity eaten and how long the person live

But, the correlation does not consider those that does not consume meat, and it is very hard to determined the answer to the question.

the answer is false because there are other reasons that determined longevity of life apart from meat consumption.

3 0
3 years ago
Solve the inequality. 3 + h &lt; 0
ipn [44]

Answer:

C. h<-3

Step-by-step explanation:

3+h<0

1)You subtract 3 to get H by itself

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*You do not flip the inequality sign because you only flip the sign when dividing.

6 0
3 years ago
A sequence is defined by the recursive formula f(n+1)=f(n)-2. If f(1)=18, what is f(5)?
N76 [4]

Answer:

f(5)=10

Step-by-step explanation:

A sequence is defined by the recursive formula f(n+1)=f(n)-2

If f(1)=18, then

for n=1: f(2)=f(1+1)=f(1)-2=18-2=16

for n=2: f(3)=f(2+1)=f(2)-2=16-2=14

for n=3: f(4)=f(3+1)=f(3)-2=14-2=12

for n=4: f(5)=f(4+1)=f(4)-2=12-2=10

7 0
3 years ago
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