Which graph represents the relationship between volume and kelvin temperature for an ideal gas at constant pressure?.

Simplify: 1 + i + i^2 + i^3 +i^4 +i^5 if i^2 =-1.

Vika [28.1K]

1 + i + i ² + i ³ + i ⁴ + i ⁵ = 1 + i + i ² (1 + i + i ² + i ³)

… = 1 + i + i ² (1 + i + i ² (1 + i ))

… = 1 + i + (-1) (1 + i + (-1) (1 + i ))

… = 1 + i + (-1) (1 + i - 1 - i )

… = 1 + i

Alternatively, notice that

1 - i ⁶ = (1 - i ) (1 + i + i ² + i ³ + i ⁴ + i ⁵)

so that

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

Now, i ⁶ = (i ²)³ = (-1)³ = -1, so

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

… = 2 / (1 - i )

Multiply the numerator and denominator by the conjugate of 1 - i :

… = 2 (1 + i ) / ((1 - i ) (1 + i ))

… = 2 (1 + i ) / (1² - i ²)

… = 2 (1 + i ) / (1 + 1)

… = 1 + i

3 0

2 years ago

Read 2 more answers

Who know ¿por qué constantinopla podía compararse con roma meaning

-BARSIC- [3]

de ce constantinopolii puteau fi comparați cu Roma

Explanation:

hope this helps

3 0

3 years ago

Can someone please edit this one paragraph that got a grade of 1 get a grade of 2????

mr Goodwill [35]

Answer:

the process was a little different than it was just the amount you could do not to accomplish the same answer that was in a different

Explanations:

the speaker of speaker and the speaker speaker is the speaker in the process and the senate speaker and senate to the speaker in the speaker of the

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According to C. Wright Mills, what one quality of mind do all great sociologists possess

Semenov [28]

According to C. Wright Mills, one quality of mind do all great sociologists possess is sociological imagination.

<h3>What is sociological imagination?</h3>

Sociological imagination refers to the ability of someone to form an outlook on life through their own personal experiences as they interact with members of their society over time. This outlook they form can change based on newly acquired experiences.

You can learn more about social imagination here brainly.com/question/3927775

#SPJ1

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How to take notes turning class

____ [38]

Focus on what the teacher says and read what's on the board

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