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>
Answer:
C. Te vistes a las ocho.
Explanation:
Translation: You get dressed at eight
Answer:
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Always be mindful of risks
The number of hours it would take for half of the workers to complete the same job is 96 hours.
<h3>How much does it take to 6 workers to complete the job?</h3>
It is already known 6 workers working at the same rate can complete this job in a total of 48 hours, which means each of the workers represents approximately:
- 8 hours of work (48 / 6 = 8).
<h3>What happens if the number of workers is reduced?</h3>
In this case, it expected the total of hours to complete the same job increase. Moreover, the time will proportionally increase depending on the reduction of workers. Here are some examples:
- -1/3 of workers = +1/3 of time
- -1/5 of workers = + 1/5 of time
This means by reducing the workers to half of the team (-1/2) the time will duplicate.
Note: This question is incomplete; here is the possible complete question.
All the workers on a 6 person team work at the same rate. All six members of the team, working together, are able to pour foundations in 48 hours. How many hours would this job take if only half of the team worked on this task.
Learn more about hours in: brainly.com/question/15908953