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Levart [38]
3 years ago
5

How do I find the fifth roots of i?

Mathematics
2 answers:
lilavasa [31]3 years ago
4 0
The answer is in the attachment
telo118 [61]3 years ago
3 0
Let's do it the hard way. We want to solve the equation x5−1=(x−1)(x4+x3+x2+x+1)=0. Then we are interested in solving x4+x3+x2+x+1=0. Note the symmetry: if r is a root, 1/r is also a root. Why? Thereafter, we have two ways out. First, we divide everything by x2 to get x2+x+1+ 1 x + 1 x2 =(x+ 1 x )+(x+ 1 x )2−1=u2+u−1=0. What did we do? We noted (x+x−1)2−2=x2+x−2 and substituted xu2+u=1+x−1=u. The solutions for u2+u=1 are −φ and φ−1, φ being the golden ratio. We now have two equations: x+ 1 x =−φ⟹x2+φx+1=0⟹x= ± √ φ−3 −φ 2 x+ 1 x =φ−1⟹x2+(1−φ)x+1=0⟹x= ± √ −φ−2 +φ−1 2 . You can now manipulate it to get a a+bi form. Alternatively, you can multiply (x−r)(x−r−1), divide x4+x3+x2+x+1 by it and discover which r makes remainder zero. This would be somewhat long, so I won't explictly do it, but here is the idea. Maybe can help you Or open this web http://math.stackexchange.com/questions/603332/how-can-i-find-the-fifth-root-of-unity
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lorasvet [3.4K]

The total amount of paint needed is 15 quart and it cost $41.25.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

0.0015 quart of paint to cover 1 square inch.

Let the area of the rectangle be 10000 in², hence:

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The total amount of paint needed is 15 quart and it cost $41.25.

Find out more on equation at: brainly.com/question/2972832

4 0
2 years ago
The image of a parabolic lens is traced onto a graph. The function f(x) = (x + 8)(x – 4) represents the image. At which points d
alexandr402 [8]

Answer:

x = -8 and x = 4

Step-by-step explanation:

given

f(x) = (x+8) (x - 4)

recall that at any point on the x-axis, y = 0 [i.e f(x) = 0]

hence to find where the graph crosses the x-axis, we simply substitue f(x) = 0 into the equation and solve for x

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0 = (x+8) (x - 4)

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either,

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or

(x-4) = 0 ------> x = 4 (second crossing point)

Hence the graph crosses the x-axis at x = -8 and x = 4

7 0
3 years ago
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laila [671]

Answer: 18.33 ppg

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zimovet [89]
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