![Which Number Represents A Square Root Of 3 [cos(pi/2) + I Sin (pi/2)]?](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/MqWXL71zCVe43DIpTiqE5ufnn3R25BHp.png)
Answers
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Explanation:
We use De Moivre's Theorem. It says that if you started with
[tex]z = r*\left[\cos\left(\theta\right)+i*\sin\left(\theta\right)\right][/tex]
then raising both sides to the nth power leads to
[tex]z^n = r^n*\left[\cos\left(n*\theta\right)+i*\sin\left(n*\theta\right)\right][/tex]
The term out front r is raised to the nth power. We also have copies of n inside the trig functions.
The square root operation undoes the squaring operation, so we'll be dealing with n = 2.
If you were to go through each answer choice, then you'll find that squaring choice B will lead to the original expression given.
[tex]z = \sqrt{3}*\left[\cos\left(\frac{\pi}{4}\right)+i*\sin\left(\frac{\pi}{4}\right)\right]\\\\\\z^2 = (\sqrt{3})^2*\left[\cos\left(2*\frac{\pi}{4}\right)+i*\sin\left(2*\frac{\pi}{4}\right)\right]\\\\\\z^2 = 3*\left[\cos\left(\frac{\pi}{2}\right)+i*\sin\left(\frac{\pi}{2}\right)\right]\\\\\\[/tex]
Note that working this process in reverse means we apply the square root and we'll go from the expression in choice B to the original expression again.
The complex number Z = √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a complex number in the trigonometric form:
Z = √(3[cosπ/2 + i sinπ/2])
It is required to find the square root of the complex number.
To find the square root of the complex number we can use the De Moivre's theorem:
If
Z = r[cosθ + i sinθ]
Zⁿ = rⁿ[cosnθ + i sinnθ]
Using the above theorem:
Z = √3[cos[(1/2)π/2] + i sin[(1/2)π/2]]
Z = √3[cosπ/4 + i sinπ/4]
Thus, the complex number Z = √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.
Learn more about the complex number here:
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Related Questions
Melanie got a new job through the Jones Employment Agency. The job pays $32, 400 per year, and the angency fee is equal to 45% of one months pay. How much must Melanie pay the agency?
Answers
Answer:
The answer is $1,215
Step-by-step explanation:
I did $32,000 divided by 12 (months on an year) and got $2,700 per month, now we just do 0.45 x $2,700 and thats how I got the answer!
the deer population in georgia was 450,000 in 2010, and the population doubles every 5 years. in what year will the deer population in georgia reach 1 million
Answers
Answer:
We know that in 2020 the population of deer will be 900,000 based on the given numbers. In another 5 years the population will be over 1 million (1,350,000) in order to calculate when it will reach 1 million we need to see how much growth is gained per year. I believe to obtain that information we will need to divide 450,000 by 5 that equals 90,000 a year. So if I’m 2020 the population of deer will be 900,000 than add 90,000 until you reach your 1 million marker. In this case 2021 would be 990,000 thousand so 2022 would be 1,080,000. So your answer should be year 2022. Hope that helps
Check here LOADING... for instructional material to complete this problem.
Evaluate the formula z=
p−p
pq
n when p=
388
1386, n=1386, p=0.30, and q=1−p
Answers
Answer:
-1.63
Step-by-step explanation:
Plug in the values listed into the equation
([388/1386] - 0.30) / √(0.30[1-0.30)/1386
-0.02006/0.01231
-1.63
2. It’s time for Ronda to start repaying her student loans, which are amortized over the next 10 years. Her first month’s payment due is $396. How much should she expect to pay next month?
Answers
Based on the amount that she paid in the first month, the amount Ronda will pay for the next month is $396.
When a loan is amortized, it means that one can pay it off by paying the same amount every period until they would have paid off both the loan and the associated interest.
The amortized amount contains:
A portion going towards the principal(debt )A portion going towards the interest accumulated.In conclusion, as the amount is the same every time, Ronda will have to pay the same amount of $396 the next month.
Find out more at https://brainly.com/question/12256592.
Draw a square and its diagonals. Guess the measures of these angles.
Answers
Answer:
Each angle measures 45° with diagonals
Step-by-step explanation:
The sides of a triangle are in the ratio 4:4:3.What kind of triangle is it
Answers
Answer:
Isosceles triangle. An Isosceles triangle is a triangle that has 2 equal sides and 2 equal angles
Step-by-step explanation:
Please help! It’s due today
Solve: 5|9 – 3x|– 7 = 38
Answers
Answer:
x = 0
Step-by-step explanation:
Find missing value to make a function….Thanks
Answers
Answer:
12
Step-by-step explanation:
First find the slope
m = ( y2-y1)/(x2-x1)
= ( 60-30)/(6-0)
= 30/6 = 5
Now using a second set of points and the slope we can find p (0,30) and (p,90)
5 = ( y2-y1)/(x2-x1)
5 = (90-30)/(p-0)
5 = 60/p
Multiply each side by p
5p = 60
Divide by 5
p =60/5
p = 12
BRAINLIEST x 3
It is kinda late and I need to finish my work
Please help me
If you answer this I will create two other posts to give you extra brainliests
Answers
6. x=7
7. x=26
8. x=18
9. x=11 y=3
10. x=24
11. x=18 y=5
12. x= 17 y= 9
hope this helped!:)
1002828197382728173927937294729929382991divided by 182883929190.837283828281-737273728377273737272
Answers
Answer:
4.766141725565771e23
Step-by-step explanation: it is impossibel to explane so coculated it and i got 4.766141725565771e23. so there you go.
0.35 is best known as what number
Answers
re upload plz help!!!!!
Answers
Answer:
1) A) 64 tickets
B) $11
2) A) 20 rides
Step-by-step explanation:
1) a) set y to 37 because they made 37 dollars
37 = 0.50x + 5
32 = 0.50x.........subtract 5 from both sides
64 = x..................divide both sides by 0.50 to get x by itself
b) set x to 12 because x is the amount of ride tickets they bought
y = 0.50(12)+ 5
y = 6 + 5............multiply 12 by 0.50
y=11......................add
2) a) set both equations equal to each other to see when they will be equal
0.50x + 5 = 0.75x
0.50x = 0.75x - 5..........subtract 5 from both sides
0.50x - 0.75x = - 5........subtract 0.75x from both sides
-0.25x = - 5......................combine like terms
x=20...................................divide both sides by -0.25 to isolate x
The first three terms of a geometric sequence are as follows.
2, -8, 32
Find the next two terms of this sequence.
Give exact values (not decimal approximations).
Answers
Answer:
-128, 512
Step-by-step explanation:
-8/2 = -4, 32/-8 = -4, so the ratio r = -4. 32*-4 = -128, -128*-4 = 512
solve pls brainliest
Answers
The answer for a is +2.
The answer for b is +256.
Choose the expression that correctly compares 0.501 and 0.051
Answers
Answer:
0.501>0.051
Step-by-step explanation:
Answer:
0.501 > 0.051
Step-by-step explanation: blah
if you are graphing a system of equations, but the graph doesn't give you enough space to plot the y intercept or slope, what do you do? HELP ASAP
Answers
A smart watch was marked 150 and is sold at 120. Find discount percentage
Answers
Step-by-step explanation:
100 % = 150
1% = 100%/100 = 150/100 = 1.5
the discount was 150 - 120 = 30.
how many percent are in 30 ? that is our discount preventative.
30/1.5 = 20
so, the watch was sold with 20% discount.
Tarek can do a job in 4 hours. Aisha can do the same job in 6 hours. How many hours will it take the
two of them to do the job if they work together?
Answers
Answer:
it will take 10 hours
Step-by-step explanation:
6+4=10
Review the graph. On a coordinate plane, a parabola opens up and goes through (negative 2, 5), has vertex (0, 1), and goes through (2, 5). Another parabola opens to the right and goes through (8, 4), has vertex (negative 8, 0), and goes through (8, negative 4). Everything inside of the first parabola and above the second parabola within the first parabola is shaded. Which system of inequalities has the solution set shown in the graph?
Answers
Answer:
The value of h is h = -1.5
Step-by-step explanation:
The quadratic equation is represented by a parabola, the vertex form of the equation is y = a(x - h)² + k, where
(h , k) are the coordinates of its vertex point
a is the coefficient of x²
∵ The graph is a parabola opens up
∵ It has a vertex at (-1.5, 0)
∵ The vertex of the parabola is (h , k)
∴ h = -1.5 and k = 0
∵ The graph shows f(x) = (x - h)²
∵ The coordinates of the vertex are (h , k)
∵ h = -1.5 and k = 0
∴ h = -1.5
The value of h is h = -1.5
The value of h is h = -1.5
We have given that,
On a coordinate plane, a parabola opens up and goes through (negative 2, 5), has vertex (0, 1), and goes through (2, 5). Another parabola opens to the right and goes through (8, 4), has vertex (negative 8, 0), and goes through (8, negative 4).
The quadratic equation is represented by a parabola,
What is the vertex form of the parabola?The vertex form of the equation is y = a(x - h)² + k, where
(h, k) are the coordinates of its vertex point
a is the coefficient of x²
∵ The graph is a parabola that opens up
∵ It has a vertex at (-1.5, 0)
∵ The vertex of the parabola is (h , k)
∴ h = -1.5 and k = 0
∵ The graph shows f(x) = (x - h)²
∵ The coordinates of the vertex are (h, k)
∵ h = -1.5 and k = 0
∴ h = -1.5
The value of h is h = -1.5.
To learn more about the vertex form of parabola visit:
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A service call for repairing your mower is $50 plus $80 per hour.
How many hours did it take to service your mower if the charge was
$90?
0.2 hours
0.5 hours
1.125 hours
2 hours
Answers
Answer:
0.5 hours
$130 = 1h
$90 = 30m/1h
Please give me the answer
Answers
Answer:
8%
If you need the work comment on this post.
I need help pleaseeeeee
Answers
ok for the first one says
f(x)= 2 which is our Y, now we see when y is 2 our x = 1
f(x)=0 so when y= 0 , x = 2
f(1) = 2
What number has 7 as 1/10
Answers
7x10=70
So 1/10 of 70 is 7
(X-5)(X+6)
Expand and simplify
Answers
Answer:
Step-by-step explanation:
(x - 5)(x + 6) = x *(x + 6) - 5*(x + 6)
=x * x + 6 *x + x*(-5) + 6*(-5)
= x² + 6x - 5x - 30 {Combine like terms}
= x² + x - 30
Can somebody help me i've been stuck on this for awhile its because i dont get it
Answers
Answer:
15 students aren't wearing blue or white
Step-by-step explanation:
1/10 of 30 = 3
2/5 of 30 = 12
3 + 12 = 15
30 - 15 = 15
Explanation:
1/10 of 30 is 3
2/5 of 30 is 12
3+12=15
30-15=15
MODELING REAL LIFE The diagram shows the number of quarts of blood the
human heart pumps per minute,
Pumps 5
quarts of
blood per
minute
a How many quarts of blood does the human heart pump per hour?
quarts per hour
b. How many liters of blood does the human heart pump per minute?
Answers
Answer:
a)300 quarts per hour
b)4.73 (rounded to the nearest hundredth) liters or 5 (rounded to the nearest whole number liters
Step-by-step explanation:
a)f the heart pumps 5 quarts per minute, and we want it in quart per hour, all we have to do is multiply 5x60 (quarts-per-minute x minutes-per-hour) =300 quarts per hour
b)1 quart is .946liters
using that conversion we get that 5 quarts is ≈4.73 litera
Can someone help me with this?
Answers
Answer:
6 units i think but i dont u how u do it
A triangle has angles with the following measures: (x2 + 34)°, (6x + 4)°, and (10x + 10)°. Solve for x. show all work please
Answers
Answer:
[tex]x = \frac{-8 +\sqrt{190} }{2}[/tex] or x = 5.7840
Step-by-step explanation:
All the angles of a triangle add up to 180°, so we can solve this using the following equation:
180 = (x^2 + 34) + (6x + 4) + (10x + 10)
180 = x^2 + 34 + 6x + 4 + 10x + 10
Now, let's combine like terms:
180 = x^2 + (6x + 10x) + (34 + 4 + 10)
180 = x^2 + 16x + 54
Subtract 180 from both sides:
0 = x^2 + 16x - 126
And solve using the quadratic formula:
[tex]x = \frac{-b +\sqrt{b^{2}-4ac } }{2a}\\x = \frac{-16 +\sqrt{16^{2}-4(1)(-126) } }{2(1)}\\x = \frac{-16 +\sqrt{256+504 } }{2}\\x = \frac{-16 +\sqrt{760} }{2}\\x = \frac{-16 +2\sqrt{190} }{2}\\\\x = \frac{-8 +\sqrt{190} }{2}\\[/tex]
And we can approximate this as a decimal, if needed:
x = 5.7840
decrease £67 by 26% give your answer in pounds
Answers
Answer:
£ 49.58
Step-by-step explanation:
26% of 67 = 0.26 * 67 = £17.42
67 - 17.42 = £49.58
Now, you multiply
.74x67
The answer will be
£49.58
Hope this helps!!
cody spent 3 hours and 5 minutes looking for his missing cat if he finally found it at 7:35 what time was it when he originally started
Answers
Answer:
4:30
Explanation:
Three hours before 7:35 is 4:35, but you also have to subtract the extra 5 minutes to make it 4:30