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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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At the school football game, there are 42 adults

galina1969 [7]

Answer:

54 students

Step-by-step explanation:

42 / 7 = 6

9 x 6 = 54

42 : 54 = 7 : 9

4 0

2 years ago

15. If x=a Sin2t (I+Cos2t) and y=b Cos 2t (1-Cos2t) then find<br>dy/dx at =22/7*4<br>

Sav [38]

By the chain rule,

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm dt}}{\frac{\mathrm dx}{\mathrm dt}}$

It looks like we're given

$\begin{cases}x=a\sin(2t)(1+\cos(2t))\\y=b\cos(2t)(1-\cos(2t))\end{cases}$

where <em>a</em> and <em>b</em> are presumably constant.

Recall that

$\cos^2t=\dfrac{1+\cos(2t)}2$

$\sin^2t=\dfrac{1-\cos(2t)}2$

so that

$\begin{cases}x=2a\sin(2t)\cos^2t\\y=2b\cos(2t)\sin^2t\end{cases}$

Then we have

$\dfrac{\mathrm dx}{\mathrm dt}=4a\cos(2t)\cos^2t-4a\sin(2t)\cos t\sin t$

$\dfrac{\mathrm dy}{\mathrm dt}=-4b\sin(2t)\sin^2t+4b\cos(2t)\sin t\cos t$

$\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4b\cos(2t)\sin t\cos t-4b\sin(2t)\sin^2}{4a\cos(2t)\cos^2t-4a\sin(2t)\cos t\sin t}$

$\implies\boxed{\dfrac{\mathrm dy}{\mathrm dx}=\dfrac ba\tan t}$

where the last reduction follows from dividing through everything by $\cos(2t)\cos^2t$ and simplifying.

I'm not sure at which point you're supposed to evaluate the derivative (22/7*4, as in 88/7? or something else?), so I'll leave that to you.

8 0

3 years ago

What are the minimum and maximum measurements of 21 inches.

kirza4 [7]

Answer:

Step-by-step explanation:

6 0

3 years ago

Plz help asap......................................

ziro4ka [17]

Option B:

Law of cosine, two sides and the included angle are known.

Solution:

Let us first know the law of cosines and law of sines.

Law of cosine:

If we know the sides a, b and the included angle θ, then we can find the third side c. This is known as the law of cosine.

$c^2=a^2+b^2-2abcos\theta$

Law of sine:

The sides of a triangle are to one another in the same ratio as the sines of their opposite angles.

$$\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}$

Given ∠P and the sides r, q are known.

<u>To find the value of p:</u>

Option A: Law of cosines, all sides are known.

It is false by the above definition of law of cosine.

Option B: Law of cosine, two sides and the included angle are known.

It is true by the above definition of law of cosine.

Option C: Law of sines, all sides are known.

It is false, because one angle is given in question.

Option D: Law of sines, two angles and the included side are known.

It is false, because two angles are not given.

Option B is the correct answer.

Hence the answer is "Law of cosine, two sides and the included angle are known".

7 0

3 years ago

What is the domain of the function represented by the graph? A graph shows an upward parabola on a coordinate plane vertex at (m

vlabodo [156]

Using it's concept, the domain of the function represented by the graph is all real numbers.

<h3>What is the domain of a function?</h3>

The domain of a function is the set that contains all possible input values for the function.

In this problem, a parabola is used, which has no restriction such as an even root or a fraction, hence the domain is all real values.

More can be learned about the domain of a function at brainly.com/question/10891721

#SPJ1

3 0

1 year ago