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SOVA2 [1]
3 years ago
10

Which expression is a cube root of -1+i√3?

Mathematics
1 answer:
Tpy6a [65]3 years ago
8 0

Answer:

<em>The correct option is C.</em>

Step-by-step explanation:

<u>Root Of Complex Numbers</u>

If a complex number is expressed in polar form as

Z=(r,\theta)

Then the cubic roots of Z are

\displaystyle Z_1=\left(\sqrt[3]{r},\frac{\theta}{3}\right)

\displaystyle Z_2=\left(\sqrt[3]{r},\frac{\theta}{3}+120^o\right)

\displaystyle Z_3=\left(\sqrt[3]{r},\frac{\theta}{3}+240^o\right)

We are given the complex number in rectangular components

Z=-1+i\sqrt{3}

Converting to polar form

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

\displaystyle tan\theta=\frac{\sqrt{3}}{-1}=-\sqrt{3}

It's located in the second quadrant, so

\theta=120^o

The number if polar form is

Z=(2,120^o)

Its cubic roots are

\displaystyle Z_1=\left(\sqrt[3]{2},\frac{120^o}{3}\right)=\left(\sqrt[3]{2},40^o\right)

\displaystyle Z_2=\left(\sqrt[3]{2},40^o+120^o\right)=\left(\sqrt[3]{2},160^o\right)

\displaystyle Z_3=\left(\sqrt[3]{2},40^o+240^o\right)=\left(\sqrt[3]{2},280^o\right)

Converting the first solution to rectangular coordinates

z_1=\sqrt[3]{2}(\ cos40^o+i\ sin40^o)

The correct option is C.

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a business want to increase its number of employees by 65% to 20,460. How many employees does the company currently have?
Crazy boy [7]

Answer:

12,400

Step-by-step explanation:

Let the current employees be x

65% increase in number = 0.65x

If the total number of employees after the increase is 20,460, then;

x + 0.65x = 20,460

1.65x = 20,460

x = 20,460/1.65

x = 12,400

Hence the current number of employees is 12,400

5 0
3 years ago
Which of the following best describes the solution to the system of equations below?
OverLord2011 [107]

Answer: OPTION A

Step-by-step explanation:

The equation of the line in slope-intercept form is:

y=mx+b

Where m is the slope and b the y-intercept.

Solve for y from each equation:

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As you can see the slope and the y-intercept of each equation are equal, this means that both are the exact same line. Therefore, you can conclude that the system has infinitely many solutions.

3 0
3 years ago
Abigail plays a game in which she spins a spinner over and over again. The spinner has 4 equally sized sections labeled 1 throug
Andrew [12]

Answer:

Part 1: The option (A) is correct. The prediction of the event is 32 spins.

Part 2: Option (B) is correct. The probability of the event is 139 passwords.

Part 3: The P(yellow or blue) is 2/6.

Part 4: Option (B) is correct.

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Step-by-step explanation:

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5 0
3 years ago
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Step-by-step explanation:

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3 years ago
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xeze [42]

Answer:

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Step-by-step explanation:

6 0
3 years ago
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