What do you do at a red light?

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

Anybody know this? Please help lol

insens350 [35]

B) make them feel less human

8 0

3 years ago

Which best describes the strength of the correlation, and what is true about the causation between the variables? it is a weak n

anzhelika [568]

The true statement about the causation between the variables it is a weak negative correlation, and it is not likely causal.

<h3>What is causation between the variables?</h3>

The causation between the variables shows that the occurrence of one event causes the occurrence of the other.

The informal relationship between two events.

Thus, the correct option is A, it is a weak negative correlation, and it is not likely causal.

Learn more about variables

brainly.com/question/15740935

#SPJ1

6 0

2 years ago

How does the term ""the white man’s grave"" explain why much of africa went unexplored by europeans for so long?.

Komok [63]

Answer:

This term refers to the dangers Europeans faced in Africa's interior due to disease, wild animals, and hostile tribes.

Explanation:

got it right on the quiz

3 0

2 years ago

A person’s long-lasting manner of behaving throughout a variety of situations is most likely influenced by __________.

Alexxx [7]

A person s long-lasting manner of behaving throughout a variety of situations is most likely influenced by personality traits.

7 0

2 years ago