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Kay [80]
4 years ago
15

Complex numbers & DeMoivre's theory If z=-1-√3 i and z^6=a+bi, a=_____ and b=_____

Mathematics
1 answer:
Mice21 [21]4 years ago
8 0

Convert z to exponential/polar/trigonometric form:

r=|z|=\sqrt{(-1)^2+(-\sqrt 3)^2}=2

\tan\theta=\dfrac{-\sqrt3}{-1}\implies\theta=\dfrac{4\pi}3

\implies z=-1-\sqrt3\,i=2e^{4\pi/3\,i}=2\left(\cos\dfrac{4\pi}3+i\sin\dfrac{4\pi}3\right)

By DeMoivre's theorem,

z^6=\left(2e^{4\pi/3\,i}\right)^6=2^6e^{24\pi/3\,i}=64e^{8\pi\,i}

z^6=64\left(\cos8\pi+i\sin8\pi)=64

so that a=64 and b=0.

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What is the product of 5.06 and 2.1
Oksana_A [137]

Answer:

10.626

Step-by-step explanation:

There's multiple ways to go about it. See how

5.06 * 2.1 = (5 + 0.06)(2 + 0.1) = 5*2 + 0.06*2 + 5*0.1 + 0.06*0.1 =

= 10 + 0.12 + 0.5 + 0.006 = 10.626

Please notice how breaking up the product into smaller parts has let us make all the computations without too much hassle.

7 0
2 years ago
Read 2 more answers
Write the equation of the line that's passes through (2,-3) and a slope of -5 I standard form
sashaice [31]
Y= - 5x + 7 

Use the point and slope to solve for b, which is 7. 
7 0
3 years ago
You have the numbers 1–24 written on slips of paper.If you choose one slip at random, what is the probability that you will not
ollegr [7]
The numbers that are divisible by 3 are:

3, 6, 9, 12, 15, 18, 21, 24
that is 8 numbers divisible by 3

24-8=16 numbers NOT divisible by 3

so the probability of not picking a number divisible by 3 is 16/24


hope this helps and is right :)
3 0
3 years ago
Read 2 more answers
The density of titanium is 4.51 g/cm^3
forsale [732]

The volume of titanium is 20.86 cubic inches

<em><u>Solution:</u></em>

The volume is given by formula:

volume = \frac{mass}{density}

From given,

Density of titanium = 4.51 g/cm^3

Mass = 3.4 lb

Let us convert the mass to grams

1 pound = 453.592 grams

Therefore, 3.4 pound is equal to:

3.4 \text{ pound } = 3.4 \times 453.592 \text{ grams }\\\\3.4 \text{ pound } = 1542.2128\text{ grams }

Now substitute the values into formula:

volume = \frac{1542.2128}{4.51}\\\\volume = 341.95 cm^3

Let us convert cubic centimeter to cubic inches

1 cubic centimeter = 0.0610237 cubic inches

Therefore,

341.95\ cm^3 =  0.0610237 \times 341.95\ in^3 = 20.86\ in^3

Thus volume of titanium is 20.86 cubic inches

6 0
3 years ago
A past study claims that adults in America spend an average of 17 hours a week on leisure activities. A researcher wanted to tes
8090 [49]

Answer:

The claim is false.

Step-by-step explanation:

Given the data :

13 24 21 37 15 25 18 22 40 32

The sample mean and standard deviation can ben calculated for the given sample.

Using calculator :

Sample mean, xbar = 24.7

Sample standard deviation, s = 9.04

Sample size, n = 10

The hypothesis :

H0 : μ = 17

H1 : μ ≠ 17

The test statistic :

(xbar - μ) ÷ (s/√(n))

(24.7 - 17) ÷ (9.04/√(10))

7.7 / 2.8586990

Test statistic = 2.694

We can obtain the Pvalue, at α = 0.05 ; df = n-1 = 9

Pvalue = 0.0246

Since Pvalue < α ; we reject the null ; Hence, there is significant evidence to conclude that an adult American does not spend average of 17 hours in leisure

5 0
3 years ago
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