Consider the numbers z = 3√2(cos(135°) + i sin(135o) and w = cos(180o) + i sin(180°).
Which expression is closest to the polar form of z + w?
Answers
Answer: A
5(cos(143o) + i sin(143o))
Step-by-step explanation:
The expression that is closest to the polar form of z + w is
[tex]5(cos(143^{\circ})+i~sin(143^{\circ}))[/tex]
What is complex number?"The number of the form a + ib where a, b are real numbers and [tex]i=\sqrt{-1}[/tex]"
What is polar form of the complex number?"The polar form of the complex number z = x + iy is [tex]z=r(cos(\theta)+i~sin(\theta))[/tex] where [tex]r=\sqrt{x^{2} +y^{2} } , ~\theta=tan^{-1}(\frac{y}{x} )[/tex] "
For given question,
We have been given two complex numbers.
[tex]z = 3\sqrt{2} (cos(135^{\circ}) + i~sin(135^{\circ})[/tex] and [tex]w = cos(180^{\circ}) + i~sin(180^{\circ})[/tex]
We know that,
[tex]cos(135^{\circ})\\=cos(90^{\circ}+45^{\circ})\\=-sin(45^{\circ})\\=-\frac{1}{\sqrt{2} }[/tex]
And
[tex]sin(135^{\circ})\\=sin(90^{\circ}+45^{\circ})\\=cos(45^{\circ})\\=\frac{1}{\sqrt{2} }[/tex]
So, the first complex number would be,
[tex]z = 3\sqrt{2} (cos(135^{\circ}) + i~sin(135^{\circ})\\\\z = 3\sqrt{2} (-\frac{1}{\sqrt{2} } + i~\frac{1}{\sqrt{2} } )\\\\z=-3+3i[/tex]
We know that [tex]cos(180^{\circ})=-1,~~sin(180^{\circ})=0[/tex]
So the second complex number would be,
[tex]w = cos(180^{\circ}) + i~sin(180^{\circ})\\\\w = -1 + 0i[/tex]
So, the sum of complex numbers z and w would be,
[tex]z+w\\=(-3+3i)+(-1+0i)\\=-4+3i[/tex]
We write the complex number -4 + 3i in the polar form.
Comparing above number with x + iy, we have x = -4 and y = 3
[tex]\Rightarrow r=\sqrt{(-4)^2+3^2}\\ \Rightarrow r=5[/tex]
Also, the value of [tex]\theta[/tex] would be,
[tex]\theta=tan^{-1}(\frac{3}{-4} )\\\\\theta= -36.86^{\circ}\\\\\theta=180^{\circ}-36.86^{\circ}\\\\\theta=143.14^{\circ}[/tex]
So the complex number -4 + 3i in the polar form would be, [tex]5(cos(143.14^{\circ})+i~sin(143.14^{\circ}))[/tex]
Therefore, the expression that is closest to the polar form of z + w is
[tex]5(cos(143^{\circ})+i~sin(143^{\circ}))[/tex]
Learn more about polar form of complex number here:
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Related Questions
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Practice
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100
Based on the table, how many minutes does a person need to run to burn 100 calories?
Answers
Answer:
20 Minutes
Step-by-step explanation:
Answer:
20 minutes
From the given information, we can see that:
4 minutes burns 20 calories, and
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Step-by-step explanation:
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Answer:
Yes.
Step-by-step explanation:
The x's are all different, so the set of numbers is indeed a function. Although two y's are the same, it doesn't matter.
Hope this helped you!! Have an amazing day :D
A recipe that serves 8 people requires 4 1/2 cup of flour how much do you need to serve for 24 people
Answers
Answer:
You would need thirteen and a half( [tex]13\frac{1}{2}[/tex]) cups of flour.
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answer:
one could be (7*x) (7*4)
Step-by-step explanation:
Graph the equation y=-x^2+12x-32y on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
Answers
The vertex of the quadratic function y = - x² + 12 · x - 32 is located at point (0, - 20) and the roots of the abovementioned are points (4, 0) and (8, 0), respectively.
How to graph a quadratic function
By fundamental algebra theorem we need at least three no coplanar different points to graph quadratic functions. First, we determine 5 different points, then we pass the curve through the five points and finally we identify the roots and the vertex.
If we know that (- 16, - 480), (- 12, - 320), (- 8, - 192), (- 4, - 96), (0, - 32), then the graph of the quadratic function is shown in the image.
The vertex of the quadratic function y = - x² + 12 · x - 32 is located at point (0, - 20) and the roots of the abovementioned are points (4, 0) and (8, 0), respectively.
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If you brainliest me I will friend you and text you everyday and most of all this game is called: What's In The Box? Here are some things for you to guess
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2: you can eat it
3: it starts with and H
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Answer:
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Step-by-step explanation:
An employee working for a local seafood company is delivering fresh Maryland seafood to nearby states. After 2 hours of driving, the truck has traveled 128 miles. After 3.5 hours of driving, the truck arrives at its first destination, 203 miles from home. What is the average rate of change, in miles per hour, for this trip?
Answers
Answer:
58 miles per hour
Step-by-step explanation:
Given that :
Miles traveled after 2 hours = 128 miles
Miles traveled After 3.5 hours = 203 miles
Average rate of change in miles per hour :
Total miles driven / total time taken
The average rate of change in miles per hour :
203 miles / 3.5 hours
58 miles per hour
A city has a population of 310,000 people. Suppose that each year the population grows by 7%. What will the population be after 15 years?
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240 is answer
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Answer:
x ≥ 60
Step-by-step explanation:
greater than or equal to 60
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Answer:
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Step-by-step explanation:
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Answer:
The answer should be B
Step-by-step explanation:
In a sporting goods store, the ratio of footballs to soccer balls in stock is normally 8: 5. If there are 320 footballs in stock in the store, how many soccer balls are in the store?
Answers
Answer:
200 soccer balls
Step-by-step explanation:
Proportion:
8/5 = 320/x
Cross Multiply:
320 x 5 = 1600
8 x X = 8x
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8x = 1600
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How many kilometers are in 60 miles? Note: There are 1.609kms in 1mi.
Answers
Answer:
Your answer is 96.5606 Kilometers.
Step-by-step explanation:
1.609 x 60 = 96.5606
Mark as brainliest if it's correct!
Answer:
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Step-by-step explanation:
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Answers
6/3 equals 2, so we make the left side 2.
2 = 22/x
x is being divided by 22, so to undo it, we multiply.
therefore it becomes:
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2x = 22
we can divide by 2 on both sides.
we are left with
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hope this helps!
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Answers
Complete Question
The number of successes and the sample size for a simple random sample from a population are given below. x-4, n 200, [tex]H_o[/tex]: p- 0.01, Ha p>0.01, a 0.05 . determine the sample proportion of x
Answer:
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Step-by-step explanation:
From the question we are told that
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The sample size is n = 200
The null hypothesis is [tex]H_o : p = 0.01[/tex]
The alternative hypothesis is [tex]H_a : p > 0.01[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
Generally the sample proportion of x is mathematically represented as
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Answers
Answer:
5.74
Step-by-step explanation:
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Answers
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The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
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Given data ,
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5x + 2y + 9 = 0
Now , the equation of line is expressed in the form y = mx + c
5x + 2y + 9 = 0
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Hence , The slope of the line is -5/2
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Answer:
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Stefan sells Jin a bicycle for $163 and a helmet for $17. The total cost for Jin is 150% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin? Stefan originally spent $
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Answer:
44$
Step-by-step explanation:
Answer:
Answer
5.0/5
7
PiaDeveau
Ace
5K answers
22.1M people helped
The selling cost for Stefan bicycle = $114 and
the selling cost of a helmet = $18.
The total cost for Jin is 120% of the money spent.
Let us assume purchasing cost of a bicycle = $x.
Purchasing cost of a halmet = $y.
For bicycle
120% of x is $114
=> 1.20 × x = 114
Dividing both sides by 1.20, we get
x=$95.
For helmet.
120% of y is $18.
=> 1.20 × y = 18.
Dividing both sides by 1.20, we get
y = $15.
Therefore, Stefan spent originally to buy a bike $95 and $15 to buy a helmet.
$114 - 95 = $19
$18 - 15 = $3.
Therefore, he made $19 by selling the bicycle and $3 by selling the helmet to Jin.
Step-by-step explanation:
You start at (0, 8). You move up 1 unit and right 3 units. Where do you end?
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Step-by-step explanation:
Find the rate of change for the function h(x) = 2–x on the interval –2 ≤ x ≤ -1.
0
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Rasheed wants to buy two new video games that cost $28.50 each. He earns money for them by mowing lawns in his neighborhood, and his earnings are shown in the table below. Rasheed’s Earnings Week Amount Earned 1 $7.50 2 $4.85 3 $12.25 4 $9.00 5 $8.15 How much more does Rasheed need to earn before he can buy the video games? $3.85 $13.25 $15.25 $17.00
Answers
Answer:c
Step-by-step explanation:
I just toke the quiz
Answer:
c
Step-by-step explanation:
Shaniqua brings home $250 per week working 25 hours. She is able to save $30 of her earnings each week.
Shaniqua wants to have $750 saved at the end of 15 weeks. She is allowed to work up to 30 hours per week if she
wants. She can save all the money earned working extra hours. How many hours (as a whole number) each week
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Answers
Answer: She'd have to work 27 hours a Week because by her working 2 more hours shed be able to save up 50 a week.
Explanation: 750 divided by 15 (the weeks) is 50. Shed need to save 50 a week instead of 30 to reach her goal and the amount 50 divided by the number of hours she works (25) is 2. Add the 2 to 25 and you get 27 weeks.
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240 fingers I think
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Answer:
Simple interest is calculated on the principal, or original, amount of a loan. Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods, and can thus be regarded as "interest on interest."
if f(x) = x^4+7, g(x) = x-9, h(x) = sqrt x, then
f*g(x) =
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ejeqf
Step-by-step explanation:
kmd
Solve for a.
ab +c=d
a=b/(c-d)
a = (d - C)/b
a=b+c/d
Answers
Answer:
ab +c=d
Step-by-step explanation:
just took the test
