If (x+iy)³ = y+vi then show that (y/x + v/y) = 4(x²-y²)
Answers
Answer:
Step-by-step explanation:
[tex] \large\underline{\sf{Solution-}}[/tex]
Given that,
[tex]\rm \longmapsto\: {(x + iy)}^{3} = y + iv[/tex]
[tex]\rm \longmapsto\: {x}^{3} + 3 {x}^{2}(iy) + 3x {(iy)}^{2} + {(iy)}^{3} = y + iv[/tex]
[tex]\rm \longmapsto\: {x}^{3} + 3 {x}^{2}yi + 3x {i}^{2} {y}^{2} + {i}^{3} {y}^{3} = y + iv[/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1 \: \: \: and \: \: \: {i}^{3} = - i }}} \\ [/tex]
So, using this, we get
[tex]\rm :\longmapsto\: {x}^{3} + 3 {x}^{2}yi - 3x{y}^{2} - i{y}^{3} = y + iv[/tex]
[tex]\rm \longmapsto\: ({x}^{3} - 3x {y}^{2}) + i(3{x}^{2}y- {y}^{3})= y + iv[/tex]
On comparing real and Imaginary parts, we get
[tex]\rm \longmapsto\:y = {x}^{3} - 3 {xy}^{2} [/tex]
and
[tex]\rm \longmapsto\:v = {3x}^{2}y - {y}^{3} [/tex]
Now, Consider
[tex]\rm \longmapsto\:\dfrac{y}{x} + \dfrac{v}{y} [/tex]
[tex]\rm \: = \: \dfrac{ {x}^{3} - {3xy}^{2}}{x} + \dfrac{ {3yx}^{2} - {y}^{3} }{y} [/tex]
[tex]\rm \: = \: \dfrac{ x({x}^{2} - {3y}^{2})}{x} + \dfrac{y({3x}^{2} - {y}^{2})}{y} [/tex]
[tex]\rm \: = \: {x}^{2} - {3y}^{2} + {3x}^{2} - {y}^{2} [/tex]
[tex]\rm \: = \: 4{x}^{2} - {4y}^{2}[/tex]
[tex]\rm \: = \: 4({x}^{2} - {y}^{2})[/tex]
Hence, Proved
Related Questions
(1/3) to the power of 3
Plz
Answers
Answer:
1/27
have a lovely day <3
Answer:
[tex]\frac{1}{27}[/tex]
Step-by-step explanation:
[tex]\frac{1}{3} ^3[/tex]
[tex]\frac{1}{3}[/tex] × [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{3}[/tex]
[tex]\frac{1}{27}[/tex]
Find the equation for the line that passes through the points (1, 1) And (3, 5)
Answers
Answer:
y = 2x - 1
Step-by-step explanation:
Slope = (5-1) / (3-1) = 4/2 = 2
y-intercept = 1 - (2)(1) = - 1
y = 2x - 1
If 20 apples cost N300 how many apples can be bought for N1875
Answers
Answer:
28125
Step-by-step explanation:
300÷20=15
15×1875=28125
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Answers
Answer:
A = 1
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Step-by-step explanation:
Find the product of 54 and the sum of 15
Answers
Answer:
6 and 9 are the two numbers that have a sum of 15 and when multiplied + 54
Step-by-step explanation:
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A water bucket in your backyard has a small hole in it. You notice that it drained a total of 3.5 liters
in 4 days. What is the average change in water volume each day? (hint: divide)
Answers
hello can anyone help?
Harry drives 182 miles.
His average speed is 35 miles per hour.
How long does the journey take?
Give your answer in hours and minutes.
Answers
Answer:
5 hours 12 minutes
Step-by-step explanation:
Amount of time the journey took = 182 miles ÷ 35 miles/h
= 5.2h
= 5h 12mins
Help please i need this done by tomorrow
Answers
Step-by-step explanation:
here you go I hope my answer is correct goodbye
Answer:
i think you draw it
Step-by-step explanation:
it tells you the answer
what is 843.5 x 10 with a exponent of 2
Answers
Answer:
84,350
Step-by-step explanation:
843.5 x 10^2 = answer
Answer:
84350
Step-by-step explanation:
Find the result when 68 is decreased by 50%.
Answers
Answer:
34
Explanation:
When 68 is decreased by 50%, that would mean that it is decreasing by half of that number. Half of that number would be 34 and that would be your answer.
translate seven minus three times a number into an algebraic expression
Answers
Key: x is times and X is “a number”
Any answers for this?
Answers
Answer:
D(t) = 2,280 - 60t
for D(15) compare the eqns and substitute the value of t.
D(15) = 2,280 - 60(15)
D(15) = 1,380 miles.
In the context of the qn, the Chang family travels 1,380 miles in 15 hours.
This week a pack of tomato plants cost $25 next week the plants on sale for 15% off Larissa wants to know the price of the tomato plants if she buys them next week
Answers
Step-by-step explanation:
15%25$
[tex] \frac{15}{100} \times 25[/tex]
[tex] \frac{375}{100} [/tex]
=3.75
25-3.75=21.25$
Please solve the math problem for me... I will mark you brainliest
Answers
Answer:
x = 5
Step-by-step explanation:
3x + 1 should equal 16
Answer:
X=5
Step-by-step explanation:
3x+1=16
move the 1 over to the 16 so it is 16 - 1 = 15
3x=15
Move the 3 over to where the 15 is in order to get x by itself
3/3 = x
3/15 = 5
so X should = 5
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Answers
Answer:
81+71+x=180
152+x=180
x=180-152
x=28°
Step-by-step explanation:
Hope that this is helpful.
Have a great Day.
rewrite the equation in standard form y = - 3/4x - 6
Answers
Answer:
3x + 4y = - 24
Step-by-step explanation:
Brainliest?Question 1
Tim is a car salesman and earns a 5% of the price of the cars he
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Estimate the amount Tim earned last month.
Answers
Answer:
152558.75*5%=7627.9
Step-by-step explanation:
Vicky is a cook at a diner. Before the diner opened, she used 12 eggs to make a large frittata that will be sold by the slice. She will also use 3 eggs whenever someone orders an omelet. If Vicky uses a total of 39 eggs by the end of the day, how many omelets must have been ordered?
Write and solve an equation to find the answer.
Answers
Answer:
6 is this answers to find
Answer:
9 omelets
Step-by-step explanation:
She used 12 eggs in the morning so 39-12= 27 then 27/3 = 9
Hope that helps!
NO LINKS IF YOU HAVE LINK DO NOT ANSWER PLEASE ANSWER NO LINKS Please no links will mark brainiest for complete and correct answer.
PLEASE SHOW ALL OF YOUR WORK
Solve for p
3(2p−1)−2(3p+4)=11p
Answers
Answer:
p = -1
Step-by-step explanation:
3(2p - 1) - 2*(3p+ 4) = 11p
Use distributive property: a(b +c) =a*b +a*c
3*2p -3*1 -2*3p + (-2)*4 = 11p
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6p - 6p - 3 - 8 = 11p
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Divide both sides by 11
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Answers
PLS HELP ME WITH THIS! I NEED IT RIGHT NOW!! PLSSS I'LL GIVE BRAINLIEST I PROMISE. JUST PLS HELP ME.
In 2010, an estimated 1.664 x 10⁸dollars in 1000 bills were in circulation. How many 1000-dollar bills were in circulation?
Answers
Answer:
166,400,000
Got the same one today and figured it out! Yw!❤
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Answers
Answer:
base salary
Step-by-step explanation:
f(0) means that he had no sales so the only money made would be from the base salary
so I'm not sure how to draw a square with the area of 3 units
Answers
So we can say “3 = L x L” where L is any side length of the square
L times L is just simplified to L squared: “3 = L^2”
We can take the square root of both sides to get rid of the L squared. We are left with “the square root of 3 equals L”.
Sqrt(3) = L
And on a calculator the square root of 3 is 1.73205080757.
1.73205080757 = L.
The square is 4 lines in a box each with the length of 1.73205080757 units.
Kristal was writing 5,060 in scientific notation. She said that it was 5.6 x 10^3 do you agree or disagree
Answers
Answer:
I disagree
Step-by-step explanation:
It is 5.06 x 10^3
HELP PLEASE!!!!
The 10 largest soccer and football stadiums have a capacity of at least of 1 x 105 people. Each stadium has 8 events each year for 10 years.
How many total people attended these events if every event was seated to capacity? Select ALL that apply
A
at least 80,000,000 people
B
at least 800,000,000 people
С
at least 0.8 x 107 people
D
at least 8 x 107
people
E
at least 80 x 107 people
Answers
If each stadium has 8 events each year that’s 80 events per year in total.
So there is 800 events throughout the 10 years (each year holding 80 events).
To find the total number of people that attended the event we multiply the number of people that attended each event by how many events we had in total (105x800=84000)
So, C,D and E apply.
Giving brainlyest .... .....
Answers
Answer:
4.475 is the answer.
Step-by-step explanation:
also hide your tabs just in case ;)
Answer:
4.475 believe me i did k12 before plz give me brainlyiest explanation:
Chase bought 5 chicken wings for $9.50. If Chase spent $26.60, how many chicken wings did he buy?
Please help me find the answer for this ( I think the answer is 14? I don't know for sure) thank you so much if you help me!
Answers
Find the price of 1 wing:
9.50 / 5 = 1.90 per wing
Divide total spent by price per wing:
26.60 / 1.90 = 14
Answer: 14
Answer:
14
Step-by-step explanation:
$9.50 / 5 = $1.90
$26.60 / $1.90 = 14
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Answers
Answer:
1/3125 or, 5^-5
Step-by-step explanation:
5^-1 = blank * 5^4
1/5/625= blank or, 5^-1/5^4=blank
blank=1/3125 5^-5=blank
Write the Prime Factorization of the following Numbers:
(a) 10
(b) 37
(c)25
Answers
(b) 37= 1x37
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