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2 years ago

Which would most likely interact with an open flame and cause an accident?

SAT

2 answers:

hram777 [196]2 years ago

7 0

Answer:

gas

Explanation:

Because if you mix gas and fire there will be an explosion

yanalaym [24]2 years ago

4 0

Answer:loose hair

Explanation:

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3 years ago

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

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