Let z = 0.3(cos(31°) + i sin(31°)) and w = 20(cos(18°) + i sin(18°)).
Which statement describes the geometric construction of the product zw on the complex plane?
Stretch z by a factor of 6, then rotate 18° counterclockwise.
Stretch z by a factor of 6, then rotate 49° counterclockwise.
Stretch z by a factor of 20, then rotate 18° counterclockwise.
Stretch z by a factor of 20, then rotate 49° counterclockwise.
i think the answer is B but idk
Answers
Answer:
Option (C) is correct.
Step-by-step explanation:
Given that z = 0.3(cos(31°) + i sin(31°)) and 20(cos(18°) + i sin(18°)).
The product of both the complex number is
zw = [0.3(cos(31°) + i sin(31°))] x [20(cos(18°) + i sin(18°))]
=(0.3x20)[cos(31°) x cos(18°) + cos(31°) x i sin(18°) + i sin(31°) x cos(31°)+ i sin(31°) x i sin(18°)]
Here, (0.3x20)=6, is the magnitude of zw, which is stretching of 0.3 by 20.
zw=6[cos(31°) x cos(18°) + i{cos(31°) x sin(18°) + sin(31°) x cos(31°)}+ i² sin(31°)x sin(18°)]
As i²= -1, So
zw=6[cos(31°) x cos(18°) + i{cos(31°) x sin(18°) + sin(31°) x cos(31°)} - sin(31°)x sin(18°)]
=6[{cos(31°) x cos(18°)- sin(31°)x sin(18°)} + i{cos(31°) x sin(18°) + sin(31°) x cos(31°)}]
As cosAcosB - sin A sin B = cos (A+B) and cosAsinB + sin A sos B = sin (A+B), so
zw=6[cos(31°+18°) + i{sin(31°+18°)]
Note that, initially the argument of z is 31° and after rotation of 18° in counterclockwise direction, the argument od zw is 31°+18°= 49°. i.e
zw=6(cos(49°) + isin(49°)).
So, zw can be determined by stretching z by a factor of 20, then rotating by 18° counterclockwise.
Hence, option (C) is correct.
Answer:
C: Stretch z by a factor of 20, then rotate 18° counterclockwise.
Step-by-step explanation:
Took the quiz.
Related Questions
Is 16/27 a perfect square
Answers
Answer:
No
Step-by-step explanation:
16 is a perfect square but 27 is a perfect cube
I’ll mark you if it’s right.
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Answer:
(-3, -1)
If you rotate 180, you just flip the signs.
Two vectors of lengths 4 and 6 have a dot product equal to 24. Which is true about the vectors?
They form an acute angle.
They form an obtuse angle.
They point in the same direction.
They point in opposite directions.
Answers
Answer:
no its not its b The angle between the vectors is obtuse.
Step-by-step explanation:
oh for the other one
he is right for that one but im right on the other thing for it like it
Both vectors point in the same direction.
Dot products of vector:The dot product of two vectors is given as,
[tex]a\cdot b=ab*cos\theta[/tex]
Where [tex]\theta[/tex] is angle between two vectors.
Given that, [tex]a\cdot b=24,a=4,b=6[/tex]
Substitute values in above relation.
[tex]24=4*6*cos\theta\\\\cos\theta=24/24=1\\\\\theta=cos^{-1}1=0[/tex]
Thus, both vectors point in the same direction.
Learn more about the vectors here:
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Hello could I get help with this equation
11a+100=12
Answers
Step-by-step explanation:
-8
hope it helps:-) :-) :-) :-)
Answer:
a = -8
Step-by-step explanation: Subtract 100 on both sides to isolate the variable. From there you will have 11a = -88. If you divide on both sides to cancel them out you will get you answer for the variable -8.
i need help in this pls ill give brainly im begging ya
Answers
Answer:
The answer is 27.25 dollars
help pleaseeee slope of a line~ if there are two answers ill give brainliest for sure!
Answers
Answer:
Step-by-step explanation:
The answer would be 1/3
Hope this helps :)
Solve + 8 = 12.
a =
KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK
Answers
Answer:
4
Step-by-step explanation:
Which expression is equivalent to –2(5x – 0.75)?
10x – 0.75
10x + 0.75
–10x – 1.5
–10x + 1.5
Answers
Answer:
It is the last answer
Step-by-step explanation:
HELPPPPP MEEEEEEEEEE
Answers
Answer: #1 3+x
#2 x-4
#3 6-x+10
Step-by-step explanation:
hehe hope this helps!
x - 4
x • 10 - 6
i think this is how you do it lol
A school is raising money for new desks They have collected $400 in donations
Answers
Answer:
ok
Step-by-step explanation:
In 14 minutes a plane climbs 31500 feet, at constant speed. How far had it climbed after 9 minutes ?
Answers
Answer:
20,250
Step-by-step explanation:
first you got to find out how many feet it climes per minute.
so you will divide 31500 by 14 and get 2250
then you will take 2250 and multiply it by 9 to get 20,250
without adding, find the sum (1+3+5+7+9+11+13+15+17)
Answers
Answer:
Hey buddy, here is your answer. Hope it helps u.
Step-by-step explanation:
Without adding we can find out the sum. We just need to count how many numbers are there. In this case there are 9. Then we need to sqau the number. So 9 square=81. So without adding the sum the answer is 81.
Answer:
81
Have a beautiful day! v(⌒o⌒)v
ANY MATH EXPERTS PLS HELP RN I GOT 30 MIN LEFT I'll MARK BRAINLIEST TO WHO ANSWER'S FIRST
(If you know the answer but you can't answer it put the answer in the comments pls asap)
Answers
Answer:
I'm sorry for taking an answer but what's the question? If you tell me the question in the comments I'd be happy to answer : )
Jose earns $3680 per month, of which 22% is taken out for federal and state income taxes and other required deductions. Last month he spent $775 for rent and 86.12 on clothing. What percent of his take-home pay did he spend on rent and clothing combined?
Answers
Answer: 30%
Step-by-step explanation:
Firstly, we find 22% of $3680. This will be:
= 22% × $3680
= 0.22 × $3680
= $809.60
Therefore, his take home pay will be:
= $3680 - $809.60
= $2870.40
We are further told that last month he spent $775 for rent and 86.12 on clothing. The amount combined will be:
= $775 + $86.12
= $861.12
The percent of his take-home pay did he spend on rent and clothing combined will be:
= 861.12 / 2870. 40 × 100
= 30%
Answer:
30%Step-by-step explanation:
Step one:
monthly earnings= $3680
22% of the earnings is
=22/100*3680
=0.22*3680
=$809.6
Jose's take home will be
3680-809.6
=$2870.4
Step two:
Required
percentage spent on rent and clothing
but the total cost of rent and clothing is
=775+86.12
=$861.12
percentage of rent and cloth is
=(861.12/2870.4)*100
=0.3*100
=30%
The percentage is 30% of the take home
Write down the inequality described by "six more than the value of is at least nine"and solve for x
Answers
Answer:
[tex]x\geq 3[/tex]
Step-by-step explanation:
[tex]x+6\geq 9\\x+6-6\geq 9-6\\x\geq 3[/tex]
What is 1 1/3 minus 5/6
Answers
Answer:
1/2
Step-by-step explanation:
First, convert 1 1/3 to improper fraction:
1 1/3 = 4/3
Second, make denominator the same by multiplying 4/3 by 2/2:
4/3 * 2/2 = 8/6
Third, subtract:
8/6 - 5/6 = 3/6
Fourth, simplify:
3/6 = 1/2
The correct answer for the difference between [tex]1\dfrac{1}{3}[/tex] and [tex]\dfrac{5}{6}[/tex] is [tex]\dfrac{1}{2}[/tex] .
Given expression:
[tex]1\dfrac{1}{3} - \dfrac{5}{6}[/tex]
convert [tex]1\dfrac{1}{3}[/tex] to an improper fraction:
[tex]1\dfrac{1}{3} = \dfrac{3*1 + 1}{3}[/tex]
= [tex]\dfrac{4}{3}[/tex]
Now, the expression becomes:
[tex]\dfrac{4}{3} - \dfrac{5}{6}[/tex]
To subtract these fractions,
The common denominator is 6.
Rewrite the fractions with the common denominator:
[tex]\dfrac{4}{3}*\dfrac{2}{2}[/tex]
= [tex]\dfrac{8}{6}[/tex]
The expression becomes:
[tex]\dfrac{8}{6} - \dfrac{5}{6}[/tex]
Subtract, the numerators while keeping the common denominator:
= [tex]\dfrac{8-5}{6}[/tex]
= [tex]\dfrac{3}{6}[/tex]
Divide numerator and denominator by greatest common factor (which is 3):
3 ÷ 3 = 1
6 ÷ 3 = 2
= [tex]\dfrac{1}{2}[/tex]
The correct answer is for [tex]1\dfrac{1}{3} - \dfrac{5}{6}[/tex] is [tex]\dfrac{1}{2}[/tex].
Learn more about Improper fraction here:
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Which statements are true about trapezoid ABCD and its translated image, A'B'C'D'? Select two options.
Answers
Answer:
A,D
Step-by-step explanation:
The requried, expression for the translation of trapezoid ABCD to A'B'C'D' is (x, y) ⇒ (x - 3, y +1). Options A and D both are correct.
What is the transformation of geometry over the coordinate plane?Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.
Here,
Consider trapezoid ABCD,
As we can see the trapezoid is translated 3 units to the left and one unit up,
So the expression of the given translation is given as,
(x, y) ⇒ (x - 3, y +1)
To for the trapezoid A'B'C'D'.
Thus, the requried, expression for the translation of trapezoid ABCD to A'B'C'D' is (x, y) ⇒ (x - 3, y +1). Options A and D both are correct.
Learn more about transformation here:
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Write the number of points of intersection of each pair of coplanar lines.
PLEASE HELP!!!
Answers
Answer:
A. Parallel Lines (Zero)
B. Intersecting Lines (One)
C. Coincident Lines (Infinitely Many)
The sum of four consecutive integers is 74.
What is the first integer?
16
17
19
18
Answers
Answer:
17
Step-by-step explanation:
Answer:
it is 17 my boys
Step-by-step explanation:
Have a great day or make your day great
Find the 96th term of the arithmetic sequence 1, -12, -25, ...
Answers
Answer:
a₉₆ = - 1234Step-by-step explanation:
-12 - 1 = -13 and -25 - (-12) = -13 ⇒ d = -13
[tex]a_n=a_1+d(n-1)\\\\a_1=1\\d=-13\\n=96\\\\a_{96}=1+(-13)(96-1)\\\\a_{96}=1-13\cdot95\\\\a_{96}=1-1235\\\\a_{96}=-1234[/tex]
2,550 gallons in 30 days i wish if you plz explain it.
Answers
Answer:
multiply 2,550 gallons to 30 and you will have your answer
Answer:
Step-by-step explanation:
first u will div 2550 by 30 and it will 38 gallons per day or per hour
Who do y´all think will win today Trump or Biden?
Answers
Answer:
Regaurdless of who ever wins...the world (meaning the US) will got to cr-ap tomorrow unfortuentley on my birthday their will be military on the streets and cops watching everyones every moves..
Trump wins...gunshotss
Biden wins...gunshots
Step-by-step explanation:
Why? because politics has come to the point that if your choice of party didnt win people become babies and throw tantrums on the streets and start riots...watch us start living like Bird Box frrrr
Write the equation of the line that passes through (0, 2) and (2, -4) in slope-intercept form.
a. y = -3x + 2
b. y = - 1/3x + 2
c. y = 3x - 3
d. y = -1/3x - 2
Answers
Answer:
i think its A..............
Step-by-step explanation:
A
what’s the slope for 6,14 and 10,9
Answers
Answer:
The slope is [tex]-\frac{5}{4}[/tex] .
Please help I have 20 missing assignment T-T
Answers
Answer:
Venus 170 million km
Mars 253 million km
Step-by-step explanation:
**PLEASE ANSWER** 20 POINTS, Rebeka claimed the equation 3x + 4 = 10 has two solutions. Explain the error in Rebeka’s claim.
Answers
Answer:
x=2
Step-by-step explanation:
3x+4=10
subtract four on both sides, you will get 3x=6, divide by three on both sides, x=2
What is the approximate sum of this series?
multiple choice
Answers
Answer:
D)134.83
Step-by-step explanation:
Sorry I don't know how to explain it here but the answer is D and I'm 100% sure
Darren went shopping. He bought a shirt and a tie for a total price of £29.75. This price includes a 15% loyalty discount.
Before the discount, the tie was priced at £13. Work out the price of the shirt before the discount.
Answers
Answer:
£21.21
Step-by-step explanation:
First, find the total price of the two items before the discount was applied. To do this, multiply the discounted price by 1.15, which is the decimal form of 115%. I added 15% to 100% in order to reverse to discount.
29.75 * 1.15 = 34.21
Now that we know the total price before the discount, we can subtract the value of the tie from the total price to find the price of the shirt:
34.21 - 13 = 21.21
The shirt cost £21.21 before the discount.
Hope this helps :)
Answer: Darren's shirt is £16.75. And with the loyalty discount, his total price would approximately £25.28.
Explanation:
To find the price of his shirt, you subtract the total price with the ties price. 29.75 - 13.00 which would get you 16.75. And then you have to subtract 15% from 29.75. (Original price) Once you're finished, you should get 25.28 (Unless I'm dumb) And if you need to learn how to subtract or add with percentages, you can look for a video on YT. Hope this helped!
9. Original price of a CD: $17,00 Discount: 50%
Answers
Answer:
$34.00
Step-by-step explanation:
This is because if you divide 17 by 0.50 that equalls34 the orginal price
17/0.50=34
Is this graph a function or not a function
Answers
Answer:
YEs it is a function
Step-by-step explanation:
Answer:
its a function
Step-by-step explanation:
A function from set X to set Y assigns one of Y's elements to each of X's elements.