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ra1l [238]
3 years ago
8

If

"absmiddle" class="latex-formula"> and z^{6}=a+bi, then a = _ and b = _
Mathematics
1 answer:
Luden [163]3 years ago
3 0

Rewriting z in polar form makes this trivial.

z=|z|e^{i\mathrm{arg}(z)}

We have

|z|=\sqrt{(-1)^2+(-\sqrt3)^2}=2

\mathrm{arg}(z)=\tan^{-1}(-1,-\sqrt3)=-\dfrac{2\pi}3

(not to be confused with the standard inverse tangent function \tan^{-1}x. Here \tan^{-1}(x,y) is the inverse tangent function that takes into account position in the coordinate plane; look up "atan2" for more information)

So we have

z=-1-\sqrt3\,i=2e^{-2\pi/3\,i}

Then

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

so that a=64 and b=0.

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If x= –4 and y= 3 , what is the value of x–3y2 ?
Tpy6a [65]

Answer:

-31

Step-by-step explanation:

(-4)-3(3)^2

-4-3(9)

-4-27=-31

5 0
3 years ago
Read 2 more answers
You are purchasing books summer reading for $4.50 each. Part A: Your total cost, C, depends on,The input is,and the output is,Pa
Crazy boy [7]

Answer:

Part A) see the explanation

Part B) C(12)=\$54

Step-by-step explanation:

Part A)

we know that

A relationship between two variables, x, and C, represent a proportional variation if it can be expressed in the form k=\frac{C}{x} or C=kx

Let

C ---> is the total cost (represent the output or dependent variable)

x ----> is the number of books (represent the input or independent variable)

In this problem

we have a proportional relationship between the variables x and C

Part B)  we know that

The linear equation is given by

C=kx

The constant of proportionality k is the same that the slope or unit rate of the linear equation

In this problem the constant k is given

k=\$4.50\ per\ book

so

C=4.50x

For x=12 books

substitute in the equation and solve for C

C=4.50(12)=\$54

In function notation

C(12)=\$54

5 0
3 years ago
Find the exact value of sin (arccos (3/5)). For full credit, explain your reasoning.
zloy xaker [14]
The equation for cosine is <span><span><span>cos<span>(x)</span></span>=<span>Adjacent/Hypotenuse
</span></span></span>The inside trig function is <span><span>arccos<span>(<span>3/5</span>)</span></span></span>, which means <span><span><span>cos<span>(x)</span></span>=<span>3/5</span></span></span>. Comparing <span><span><span>cos<span>(x)</span></span>=<span>Adjacent/Hypotenuse</span></span></span> with <span><span><span>cos<span>(x)</span></span>=<span>3/5
</span></span></span>
Find <span><span>Adjacent=3</span></span> and <span><span>Hypotenuse=5.
</span></span>Then, using the Pythagorean theorem, find <span><span>Opposite=?
</span></span>a² = c² - b²
a² = 5² - 3² = 25 - 9 = 16
a = √16 = 4

<span><span>Adjacent=3</span></span><span><span>Opposite=4</span></span><span><span>Hypotenuse=5
</span></span><span>
Plug in the value for sin(x) = opposite/hypotenuse

sin(x) = 4/5 </span>
6 0
3 years ago
jefferson got a hit 30% of the 240 times he went to bat during the season write 30% as a reduced fraction and then find the numb
nekit [7.7K]
30% just means 30/100 which can be simplified to 3/10. In order to find the number of hits you just need to multiple .3 by the total attempts, being 240, which comes out as 76.
5 0
3 years ago
Divide 630 by 5 using partial quotients
ZanzabumX [31]
630 divided by 5 is 126

5 0
3 years ago
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