Suppose z is a complex number (a point in the plane) with angle 30 degrees and radius 2. Suppose w is a complex number with angle 60 degrees and radius 5. If z and w are multiplied together the angle of their product is how many degrees?

Answer value

Answers

Answer 1

Write each number in complex polar form:

[tex]z=2e^{i\cdot30^\circ}[/tex]

[tex]w=5e^{i\cdot60^\circ}[/tex]

When you multiply two exponential expression with the same base (here, that's e), you end up adding the exponents, so that

[tex]zw=(2\cdot5)e^{i\cdot30^\circ+i\cdot60^\circ}=10e^{i\cdot90^\circ}=10i[/tex]

so the angle of the product zw is 90°.


Related Questions

What is the length of AC?
Round to one decimal place.
4.3
D
?
4.1
8
A
B
5.3

Answers

Answer:

5.5

Step-by-step explanation: :D

40 + (52 – 7) - 4 in algebra

Answers

ANSWER ⇒ 80EXPLANATION ⇒ To solve this we can use PEMDAS, first subtract in the parentheses, than add, then finally you can subtract...YOUR ANSWER SHOULD BE 80

I think this is right, but sorry if I am wrong.[tex]GODBLESS[/tex]

PLEASE HELP!!!!!!!
A sea otter is underwater. Its position below sea level changes by −73.5 ft. in 3 minutes. What is the average change in the otter's position each minute?

Is the otter going deeper or toward the surface of the water? Show your work. Explain your reasoning.

Answers

Answer:

24.5

Step-by-step explanation:

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plz give brainliest

,54466788999 divide by 9,445 9,965 / the decimal 320​

Answers

Answer:

2123 efs d

Step-by-step explanation:

fsdfesd 2 23 r  efsdfe sde34 2df

Jenna’s Mother is shopping for energy drinks and 12 ounce bottles for Jenna
soccer team. Store a sells a case of 18 bottles for $10

Answers

Answer:If we have to find out how much ounces are in a case the answer is 216 ounces because I don’t know the question.

Step-by-step explanation:

The fire department has seen an increase in smoke detector sales since 2015. In 2015,
they sold 350 detectors which is up from the previous year by 105%. How many did they
sell in the previous year?

Answers

Answer:

Step-by-step explanation:

Given the amount of detectors sold in the current year = 350

percent increment = 105%

To get the amount sold the previous year, we will use the expression;

(105% of x) + x =  350

1.05x = 350 + x

1.05x + x = 350

2.05x = 350

x = 350/2.05

x = 170.7

Hence the amount sold the previous year was 170.7 detectors

An investment portfolio offers a plan that will increase your holdings 30%

half the time, and lose you 20% the other half. Is this a worthwhile

investment for 1) one year, and 2) for the long term?

Answers

Answer:

It is a worthwhile investment for both one year and for the long term.

Step-by-step explanation:

While the investment will obtain in the first half of the year gains of 30%, and in the second half of the year losses by 20%, at the end of the year the benefit obtained by the investment will be greater than 0%. Therefore, both within a year and in the long term, it is a viable and favorable investment, since it will yield positive results at the end of the cycle.

So, for example, an initial investment of $ 100 would operate in the following way:

-First half of the year: 100 x 1.3 = 130

-Second half of the year: 130 - (130 x 0.2) = 104

Thus, at the end of the year a profit of 4% of the initial investment will be obtained.

Please help me it’s due at 11:59pm today please help me will mark the brainiest please

Answers

Answer:

x=24

Step-by-step explanation:

2/3x+7=23

2/3x=16

x=24

IS 8 BY -3 A NEGATIVE RATIONAL NUMBER

Answers

Answer:

Yes. The answer is -24.

Step-by-step explanation:

Hope this helped.

Last weekend, nina mowed lawns and received $60. This weekend she mowed 6 lawns and received $90. what is the constant of proportionality?

Answers

Answer:

$15

Step-by-step explanation:

It is given that,

Last weekend, Nina mowed 4 lawns and received $60. This weekend she mowed 6 lawns and received $90.

We need to find the constant of proportionality.

First we can find the money received when she mowed 1 lawn for last weekend.

4 lawns = $60

1 lawn = $15

Then, we will find the money received when she mowed 1 lawn for this weekend.

6 lawns = $90

1 lawn = $15

Hence, the constant of proportionalityis $15.

Do you guys know this.

Answers

Answer:

0.77

Step-by-step explanation:

You solve the inner first, then move to the outer.

Plug in x = 20 for g(x) = [tex]\frac{2x+2}{x-6}[/tex]. It should give you [tex]\frac{42}{14}[/tex], which simplifies to 3.

You then need to solve f(x) with the given value from g(x), which is 3.

Plug in x = 3 for the equation [tex]\sqrt{0.4x^2-x}[/tex], and you should get [tex]\sqrt{0.6}[/tex].

The answer is roughly 0.77.

To compare investments, analysts convert monthly, quarterly, semiannual rates to annual rates. If an investment of $100,000 is invested at 4.5% twice a year, compounded semiannually, the growth can be modeled by the equation A(t) = 100,000(1.045)2t. What is the equivalent annual growth rate for this investment (rounded to the nearest hundredth of a percent) and what is it worth (rounded to the nearest thousand dollar) after 15 years?

2.23% and $139,000
15.01% and $194,000
9.21% and $375,000
9.01% and $364,000

Answers

I think it’s d I’m not completely sure

which model represents a fraction greater than 3/5? ​

Answers

Answer:

The last one is your answer :))

Step-by-step explanation:

Answer:

Blue circle.

Step-by-step explanation:

I hope it helps, if my answer is correct, please give BRAINLEST!

Find the unit rate and slope of the graph (ignore what I put down)

Answers

Answer:

slope: 5/7

0.714 mile per hour

Step-by-step explanation:

slope: find the point where the line is right on the line graph, put y/x which is 10/14 make the fraction smaller which is 10/14 = 5/7(I divide the denominator and nominator by 2)

Mile per hour: 5/7 cross multiply with x/1, make into an equation:

7x=5 x 1

7x = 5

x = 0.714

What is B^y=x in logarithmic form?

Answers

Answer:

The logarithmic function for x = 2y is written as y = log2 x or f(x) = log2 x. The number 2 is still called the base. In general, y = logb x is read, “y equals log to the base b of x,” or more simply, “y equals log base b of x.” As with exponential functions, b > 0 and b ≠ 1

Step-by-step explanation:

ttygytex x so r5f3ygthttg

whats inequalities ?

Answers

Answer:

An equation looks something like this: 4x2=8

In an equation each value on the opposite side of the equal sign is equal unless its unsolved and u need to solve it.

In an inequality, a <, >,  ≥ or ≤ separates 2 values that are unequal. < is a less than sign, > is a greater than sign and so on and so forth. An inequality gives all possible answers for an equation. For example 3x+2≤ 8 is showing us that 3x+2 is any value below or equal to 8. ≤ is a less than OR equal too sign.

in the equation 4x-5≤15 the inequality is showing us that 4x-5 is every possible value below or equal to 20. So an answer could be 19, 18, -5, 7 and basically every number below or equal to 20.

Step-by-step explanation:

What is the range of the function represented by the table?


A 2-column table with 5 rows. Column 1 is labeled x with entries 2, 4, 6, 8, 10. Column 2 is labeled y with entries 2.5, 5.0, 7.5, 10.0, 12.5.

{2, 4, 6, 8, 10}

{2.5, 5.0, 7.5, 10.0, 12.5}

{2, 2.5, 4, 5.0, 6, 7.5, 8, 10, 12.5}

{0.0, 0.5}

Answers

Answer:

{2.3, 5.0, 7.5, 10.0, 12.5} Option b

Step-by-step explanation:

Domain is the input values and the range is the output values. The y values.

Answer:

b

Step-by-step explanation:

Which set of side lengths cannot make a triangle?
1.) 3 cm, 3 cm, 6 cm
2.) 3 cm, 4 cm, 5 cm
3.) 3 cm, 5 cm, 7 cm
4.) 3 cm, 6 cm, 6 cm

Answers

Answer:

Option "A" is correct answer to the following question.

Step-by-step explanation:

We know that, in triangle sum of two smaller lines ≥ largest side

So,

3 cm + 3 cm < 6 cm   [Not correct to the given situation.]

3 cm + 4 cm > 5 cm [Correct]

3 cm + 5 cm > 7 cm [Correct]

3 cm + 6 cm > 6 cm [Correct]

Answer:

A  The one that says 3 cm, 3 cm, 6 cm.

Step-by-step explanation:

f(x) = 5/4a3 – 3a2 + 1/3a y g(x)= 2/5a3 + 3/4a - 6/5 ???
urgent!!

Answers



I believe this is the answer if you need it in this order.

Please answer the 2 questions from the questions on top... (8TH GRADE MATH?!)

Answers

Answer:

6. should be C and 7. should be A

Each line represents a proportional relationship. Write an equation for each line. Show your work.

Answers

JOE MAMA

HA GOTTEM

GEEEEEEEEEEEEET DUNKED ON

An adult elephant that is 10 ft tall casts a shadow that is 15 ft long. Find the length of the shadow that is a 8 ft telephone booth casts.
A. 7ft
B. 12 ft
C. 23 ft
D. 5 ft

Answers

Answer:

12 feet long bc of cross multiplying then dividing the product by 10 which gives you 12!

a. Identify at least three cases in your daily life/work where the analytics could be applied.
b. Choose one of the cases and describe how you will approach the problem. For example, you can start from where/how you collect data, how to use the data, what kind of problem can be solved, and etc.

Answers

Explanation:

Remember, the term analytics (or data analytics) refers to the act of carefully examining raw data in other to observe if there are any trends.

a) The following are three cases in our daily life/work where analytics could be applied:

analyzing changes in cell phone charges based on call durationanalyzing changes in our sleeping pattern based on hours spent on electronic gadgetsanalyzing changes in train ticket sales based on the time of the day.

b) For example, to analyze changes in my sleeping patterns based on hours spent on electronic gadgets, I need to first know

how many hours of sleep do I have every day in a particular period of time,how many hours have I spent on electronic gadgets daily for a period of time,Next, I need to answer based on the data; Is the amount of hours I sleep lower than expected? or Do I spend more time on electronic gadgets than sleep?

Juile sorted 52 sports cards. She divided into 5 equal groups. Juilie had 12 cards left over. How many cards were in each group?

Answers

Answer:

A standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards.

Step-by-step explanation:

Hope this helps!

Answer:

8

Step-by-step explanation:

52-12=40

40/5=8

Gcf and distributive property 60-50

Answers

Answer:

bvbhv hacvhkbqwdvwcqbkvwlpbjqcs[lvdcsbhk fveo fveqo fbveq wveqkneqv veq  fko nwvd vd

Step-by-step explanation:

Answer:

60=  3(2) and 5(2)

50= 5 and 2(5)

Step-by-step explanation:

Five country music bands and 3 rock bands are signed up to perform at an all-day festival. How many different orders can the bands play in if the following conditions apply?
(a) there are no restrictions on the order
(b) all the bands of each type must perform in a row

Answers

Answer: A) 40320

Step-by-step explanation:

Charlie's utility function is U(A, B) = AB, where A and B are the numbers of apples and bananas, respectively, that he consumes. When Charlie is consuming 20 apples and 80 bananas, if we put apples on the horizontal axis and bananas on the vertical axis, the slope of his indifference curve at his current consumption is:____________a. -8.b. -1/4.c. -20.d. -4.e. -1/8.

Answers

Answer:

D. -4

Step-by-step explanation:

The formula for calculating the slope of his indifference curve at his current consumption is expressed as:

M = -∆y/∆x

∆y is the change in y axis

∆x is the change in x axis

Since apples are put in the horizontal axis, ∆x = 20

Since banana are on the y axis, then ∆y = 80

Substituting the given values into the formula

M = -80/20

M = -8/2

M = -4

Hence the slope of his indifference curve at his current consumption is -4.

Option D is correct.

David made an error when determining the product of (–2.5)(–8.3). Step 1: (–2.5)(–8.3) = (–8.3)(–2.5) Step 2: = (–8.3)(–2) + (–8.3)(–0.5) Step 3: = (–16.6) + (–4.15) Step 4: = –20.75 In which step did David make his first error?​

Answers

Answer:

David make his first error at Step 3

Step-by-step explanation:

We need to determine the error David made when finding the product of (-2.5)(-8.3)

He did the following steps

Step 1: (–2.5)(–8.3) = (–8.3)(–2.5)

Step 2: = (–8.3)(–2) + (–8.3)(–0.5)

Step 3: = (–16.6) + (–4.15)

Step 4: = –20.75

David made a mistake in Step 3

When we multiply (-1) with (-1) we get + instead of - sign. The correct step 3 would be:

Step 3: =(16.6)(4.15)

Step 4: =20.75

So, David make his first error at Step 3

00:0
A toy shop purchases 125 identical stuffiedi animals for a total cost of $312.50 and sells them for $7 each
What is the percent markup?
%

Answers

Answer:

They marked it up 30 cents

Step-by-step explanation:

you do 312.50 divided by 125. Then you get 2.50. Then you multiply 7 times 125 then you get 2.80. Finally you do 2.80 minus 2.50 which equals 30 cents.

I am having trouble finding this out will anyone help?

Answers

Answer: g = 4

Step-by-step explanation:

30 = 26+g

4 = g

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