for two complex numbers z and w, which diagram shows the geometric representation of zw
Answers
Answer:
The answer is the last one, D, pictured above on the question, I took the test and it showed it was the right one
Step-by-step explanation:
The geometric expression of two complex number is the magnitude r₁*r₂ and the phase is θ₁ + θ₂.
What is complex number?The complex number is" the combination of real numbers and an imaginary number. The complex number is of the form a + i b".
According to the question,
z, w are the two complex numbers. The distance from its point in the complex plane to the origin (0,0) and the angle formed by the line segment from the origin to the point and the positive half of the x-axis.
The distance or 'magnitude' to the origin is denoted as 'r' and the angle or 'phase' formed denoted as 'θ'. The distance to the origin is called 'magnitude'.
The parameter 'r' and 'θ' related to 'a' along x-axis and 'b' along y-axis.
Euclidean distance formula applying Pythagorean theorem we have
r = [tex]\sqrt{a^2+b^2}[/tex].
The sine angle is defined to the ratio y-coordinate 'b' to length 'r' and the cosine angle is defined to the ratio x-coordinate 'a' to length 'r'.
sin θ = [tex]\frac{b}{r}[/tex] and cos θ = [tex]\frac{a}{r}[/tex].
b = r sin θ; a = r cosθ
When multiplying two complex numbers we by multiplying magnitude together and add two phase. when divide two complex number by dividing the magnitude correspondingly and subtracting the phase from the numerator and the denominator.
Then we have product complex number to the magnitude r₁ and phase θ₁
with a complex number to the magnitude r₂ and the phase θ₂ which gives the complex number with magnitude r₁ * r₂ and θ₁ + θ₂.
Hence, the geometric representation of z w is with magnitude r₁*r₂ and phase is θ₁ + θ₂.
Learn more about complex numbers here
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Related Questions
Keeley ordered 240 T-shirts to sell at the school carnival. She paid $3.20
per shirt, plus 5% of the total order for shipping. When she sells each T-
shirt at the carnival, she adds a 150% markup to the total price she paid for
the shirt (including the cost of shipping). What is the selling price of each T-
shirt?
Answers
Answer:
We have 200 shirts
Cost $2.80 each
plus a 5% charge for shipping.
Selling price
150% markup
Recall when we use percentages, we need to express them as decimals.
Michelle's cost for each shirt was
2.80 (1.05) = 2.94
The markup is
2.94 (1.50) = 4.41
The markup is added to the cost to get the final selling price.
2.94 + 4.41 = $7.35
Michelle will sell each shirt for $7.35.
Let’s reword the question to make it simpler to understand:
Keeley pays $3.20 per shirt + 5% for shipping.
She sells them at the carnival for 150% the price she paid.
First of all we should work out how much the 5% shipping cost Keeley.
If the shirts are $3.20 that means 10% is $0.32, to get 5% we divide that by 2. This means 5% is $0.16, therefore shipping is $0.16.
The total price Keeley pays per shirt is $3.20 + $0.16 = $3.36.
Now let’s find out 10% of $3.36, which is $0.336, then multiply that by 15 to get 150%:
5.04
Therefore Keeley sells each shirt for $5.04
Select the table that represents a linear function. (Graph them if necessary)
Answers
Answer:
b
Step-by-step explanation:
Q1.is the given value of the variable , s, a solution to the inequality?s > -2.25; s = -2.2
1.yes 2.no
Q2.which value of the variable is a solution of the inequality?t > -7
1. -9
2. -8
3. -7
4. -6
Answers
Answer:
1.Yes
Step-by-step explanation:
A club has four officials : president, vice-president, secretary, and treasurer. If a member cannot hold more than one office, in how many ways can the officials be elected if the club has - (12 members) *
Answers
Answer:
votes
Step-by-step explanation:
ANSWER THIS PLEASEEEEES
Answers
In triangle DEF, P is the centroid and J is the midpoint of side EF. If the length of DP is 22, what is the length of DJ?
Group of answer choices:
A. 11
B. Asparagus
C. 22
D. 33
Answers
A
SMART PEOPLE HELP PLZ!! FAST!!! I'll GIVE BRAINLY!!!! 10 POINTS!!!!
In a blind taste test, 25 people choose brand A, 15 people chose brand B, and 10 people chose brand C. There are 200 more people to be surveyed. Based on the data, which is MOST LIKELY to happen?
A. about 30 more people will choose brand C.
B. About 30 more people will choose brand A than brand B.
C. About 10 more people will choose brand B than brand C.
D. About 100 more people will choose brand A.
Answers
Answer:
pretty sure either b or d
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Since 50% of the people chose A with the first group of surveyed people, 100 more will choose that because 125 is half of 250
Estimation helps you check your answer by seeing if the estimate is close to the result you got. ... Estimation is useful when finding actual products and solving real-world problems because if your actual answer is close or exactly what you had estimated your answer will most likely be correct.
Answers
Answer:
Estimation is useful when finding actual products and solving real-world problems because if your actual answer is close or exactly what you had estimated your answer will most likely be correct.
Answer:
nuggts
Step-by-step explanation:
a window washer cleaned 28 windows in 4 hours. At this rate how many windows did he clean in 9 hours
Answers
Answer:
63
Step-by-step explanation:
28/4 = 7 windows per hour
7 × 9 = 63 windows in 9 hours
a 24 ounce of cornflakes costs $ 4.59 please help i will appreciate it thank you
Answers
Answer:
Sorry but you did not add the question.
Step-by-step explanation:
If the transformation was a rotation, tiffany can or cannot be certain the trapezoids are congruent?
Answers
Answer: Tiffany can be certain the trapezoids are congruent.
Step-by-step explanation: Two figures are congruent when their corresponding angles are equal and they have the same shape and size.
A figure can go thorugh 3 types of transformations:
Rotation: the figure is turned around a fixed point;Reflection: is created by fliping over the figure over a line;Translation: move the figure to another location, without changing its size;As long the figure doesn't change its size or shape, it doesn't matter if it's rotated, reflected or translated, they will be congruent.
When the trapezoid was rotated creating another one, the two shapes didn't change its size or shape, so Tiffany can be certain they are congruent.
find the slope of the line graphed
Answers
Answer: it would be C, -5/3
since slope = rise/run, or y2-y1/x2-x1 (either way works)
Answer:
the answer is C
Step-by-step explanation:
slope = rise/run, or y2-y1/x2-x1
You rise 5 to get to the point thats on the Y axis and you run left 3 to hit the point on the Y axis, so since you had to run left, that means its going to be negative but if you run right, the answer will be positive. i hope that helped :)
Brian rented a truck for one day. There was a base fee of $20.95, and there was an additional charge of 90 cents for each mile driven. Brian had to pay $254.05 when he returned the truck. For how many miles did he drive the truck?
Answers
Answer:
Step-by-step
Answer:
254.05 - 20.95 = 233.10 / .90 = 259
Step-by-step explanation:
The formula to convert a temperature from degrees Fahrenheit (F˚) to degrees Celsius (C˚) is C˚=59F˚−1609. 1) Write a formula to convert from degrees Celsius to degrees Fahrenheit by solving for F˚ in the equation above. 2) Are the equations from the problem statement and from part 1 inverses? EXPLAIN
Answers
Answer:
Step-by-step explanation:
Given the formula to convert a temperature from degrees Fahrenheit (F˚) to degrees Celsius (C˚) as C˚=5/9F˚−1609.
To write the formula to convert °C to °F , we will make °F the subject of the formula
Add 1609 to both sides of the equation
C˚+1609=5/9F˚−1609.+1609
C+1609 = 5/9F
Cross multiply
9(C+1609) = 5F
Divide both sides by 5
9/5 (C+1609) = F
Hence the formula to convert from degrees Celsius to degrees Fahrenheit is 9/5 (C+1609) = F.
B) To check whether they are inverses we need to check if F(C) = C(F)
To get F(C) we will substitute F into C as shown;
F = 9/5 (C+1609)
C˚=5/9F˚−1609.
F(C) = 9/5 ((5/9F˚−1609.)+1609)
F(C) = 9/5 * 5F/9 -1609 + 1609
F(C) = 9/5 * 5F/9
F(C) = 45F/45
F(C) = F
Similarly for C(F)
C(F) = (5/9(9/5 (C+1609))˚−1609.
C(F) = (C+1609) - 1609
C(F) = C
This shows that both equations are inverses of each other
What makes an equation with an inequality symbol true?
Answers
Answer:
In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥. ... If the statement is true, the number is a solution to the equation or inequality.
Step-by-step explanation:
write the equation of a line in slope-intercept form that has a slope of 2/3 and a y-intercept of (0,4)
Answers
Answer:
2/3+0x4=2/3
Step-by-step explanation: that was math right there
2(P +1) + 3(P + 2 ) > 2
need help pls
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
Given the expression
[tex]2\left(P\:+1\right)\:+\:3\left(P\:+\:2\:\right)\:>\:2[/tex]
solving the expression
[tex]2\left(P\:+1\right)\:+\:3\left(P\:+\:2\:\right)\:>\:2[/tex]
as
[tex]2\left(P+1\right)+3\left(P+2\right)=5P+8[/tex]so the expression becomes
[tex]5P+8>2[/tex]
subtracting 8 from both sides
[tex]5P+8-8>2-8[/tex]
[tex]5P>-6[/tex]
Dividing both sides by 5
[tex]\frac{5P}{5}>\frac{-6}{5}[/tex]
[tex]P>-\frac{6}{5}[/tex]
Therefore,
[tex]2\left(P+1\right)+3\left(P+2\right)>2\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:P>-\frac{6}{5}\:\\ \:\mathrm{Decimal:}&\:P>-1.2\\ \:\mathrm{Interval\:Notation:}&\:\left(-\frac{6}{5},\:\infty \:\right)\end{bmatrix}[/tex]
The graph is also attached below.
Next week your math teacher is giving a chapter test.
The test will consist of 35 questions. Some problems
are worth 2 points and some problems are worth 4 points.
There are 20 questions worth 2 points. How many
problems of 4 points are on the test?
I
November 12: 4-1. Solving Page
2
Answers
Answer:
15
Step-by-step explanation:
35-20= 15
What is the radius of a circle that has a circumference of 3.14 meters?
Answers
Answer:
.5 meters
Step-by-step explanation:
to find the circumference the equation is C = 2(pie)r so if you have known circumference you would go circumferece (3.14) divided by 3.14(pie) times 2 to find the radius which is .5
Answer:
r=0.5m
=is suppposed to be wavy
Step-by-step explanation:
Which equation can be used to solve for x in the diagram?
HELP ASAP!!
Answers
5x+3x=180
This is because a straight line is 180 degrees and and both 5x and 3x make a straight line of 180
Need help ASAP need to know if these questions are SSS,AA,SAS, or none. Plz only answer if 100% correct.
Answers
Answer:
9: AA
10: NONE
11: SAS
12: AAA
Step-by-step explanation:
Just look my man
Eli's bill at a restaurant is $54.00 before tax. He decides to leave a 20% tip. The tax rate is 8%. Which statements are correct? A) Tax on the bill is $4.32. B) The total bill is $69.12. C) The total bill is $71.28. D) Tax on the bill is $12.96. E) Eli tips the waiter $10.80.
Answers
Answer:
the correct answer would be 10.8
Answer:
ok the correct answer are $4.32, 69.12, and 10.80
Step-by-step explanation:
what is the slope of (1,3) and (2,-4)
Answers
Answer:
1/-7x
Step-by-step explanation:
All you have to do is find the distance between both points.
Determine the constant of proportionality in the situation below.
Seven water bottles cost $14.28
Answers
Do division 14.28 divided by 7 = 2.04 :DStep-by-step explanation:
0.002 in standard form
Answers
Answer:
0.9
Step-by-step explanation:
im correct 100
HELP PLEASE will mark brainly
Answers
Answer:
.6 is more than 1/2
.34 is less than 1/2
.812 is more
.9 is more
.099 is less
Step-by-step explanation:
1/2 as a decimal is .5 so anything larger than it will be .51 or greater and anything less will be .49 or less
Answer:
.6 is more than 1/2
.34 is less than 1/2
.812 is more than 1/2
.9 is more than 1/2
0.99 is more than 1/2
Step-by-step explanation: What is 1/2? 0.5. Look at the tenths place. Is the tenth higher than 5 or less than 5? But here is a warning: If you are comparing 1/2 and 1.4, 1.4 is greater than 1/2 because 1/2 is less than 1.
hi! can someone please help me i would appreciate it
Answers
Answer:
9
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
3^5=243
3^3=927
243/9=9
What is the shape of f(x)
Answers
f(x) is concave down on an interval I if all of the tangents to the curve on I are above the graph of f(x)
Helphelphelphelphelp
Answers
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
You have to add you exponents and the missing exponent which is 14 plus 2 equals 16
3x-2y if x =6 and y= -3
What's the answer?
Answers
Answer:
24
Step-by-step explanation:
3x-2y
3(6)-2(-3)
18-(-6)
18+6
24
Answer:
The answer is 24.
Step-by-step explanation:
3x-2y if x =6 and y= -3
3 times 6 equals 18
2 times -3 equals -6
18-(-6)=24
