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3 years ago

Find all complex number solutions of x^5-1=0

Mathematics

1 answer:

trasher [3.6K]3 years ago

3 0

Answer:

See below.

Step-by-step explanation:

x^5 = 1

x = 1^1/5.

We want the five complex roots of 1:-

Writing in polar form we have:

1 ^ 1/5 = cos(2πk/5) + isin(2πk/5)

The 5 solutions are found by setting k = 0, 1, 2, 3 and 4.

First one = cos 0 + i sin 0 = 1

Second = cos (2π/5 + isin(2π/5)

= 0.3090 + 0.9511i.

The other 3 can be calculated in the same way.

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Emma is standing 10 feet away from the base of a tree and tries to measure the angle of elevation to the top. She is unable to g

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The complete question in the attached figure

step 1
find the tree height for an angle of elevation of 55°
tan 55°=opposite side angle 55°/adjacent side angle 55°
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step 2
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Part 1) 4.2 ft

the value is not in the interval [14.26,37.32]
therefore
it is Not Reasonable

Part 2) 14.7 ft

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therefore
it is Reasonable

Part 3) 24.4 ft

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therefore
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Part 4) 33.9 ft

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therefore
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Part 5) 39.1ft

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therefore
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