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Vanyuwa [196]
3 years ago
6

I WILL GIVE THE CORRECT PERSON BRAINIEST

SAT
2 answers:
jarptica [38.1K]3 years ago
6 0

Answer:

C.

Explanation:

Have a good one!

mark the answer above brainliest!

attashe74 [19]3 years ago
5 0

Answer: C.) The actions of consumers in response to changes in price.

Explanation:

The Law of Demand states that as the price of a service/product decreases, the demand will increase and vice versa. Therefore, it doesn't necessarily related to the producer's response, but the consumer's. And since the consumer isn't producing, they are not in direct contact with the production costs.

I hope this helped !

Good luck <3

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1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = 1 + <em>i</em> + <em>i</em> ² (1 + <em>i</em> + <em>i </em>² + <em>i</em> ³)

… = 1 + <em>i </em>+ <em>i</em> ² (1 + <em>i</em> + <em>i</em> ² (1 + <em>i</em> ))

… = 1 + <em>i</em> + (-1) (1 + <em>i</em> + (-1) (1 + <em>i</em> ))

… = 1 + <em>i</em> + (-1) (1 + <em>i</em> - 1 - <em>i</em> )

… = 1 + <em>i</em>

<em />

Alternatively, notice that

1 - <em>i</em> ⁶ = (1 - <em>i</em> ) (1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵)

so that

1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = (1 - <em>i</em> ⁶) / (1 - <em>i</em> )

Now, <em>i</em> ⁶ = (<em>i</em> ²)³ = (-1)³ = -1, so

1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = (1 - (-1)) / (1 - <em>i</em> )

… = 2 / (1 - <em>i</em> )

Multiply the numerator and denominator by the conjugate of 1 - <em>i</em> :

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

… = 2 (1 + <em>i</em> ) / (1² - <em>i</em> ²)

… = 2 (1 + <em>i</em> ) / (1 + 1)

… = 1 + <em>i</em>

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