Express as a complex number in simplest a+bi form:
7-8i/-5+3i
[tex] \Large{\boxed{\sf z= -\dfrac{59}{\: 34} + \dfrac{19}{34}i}} [/tex]
[tex] \\ [/tex]
Explanation:To express the given complex number in a + bi form, also known as algebraic form, we will need to define what the conjugate of a complex number is.
[tex] \\ [/tex]
What is the conjugate of a complex number?[tex] \\ [/tex]
[tex] \textsf{Let z be our complex number, and} \: \overline{\sf z} \: \textsf{its conjugate.} [/tex]
[tex] \\ [/tex]
The conjugate of z, [tex] \overline{ \sf z}, [/tex] is the complex number formed of the same real part as z but of the opposite imaginary part.
Since a is the real part of z, and b is its imaginary part, this can be expressed as:
[tex] \sf If \: z = a + ib \:, then \: \overline{ \sf z} = a - ib [/tex]
[tex] \\ [/tex]
Let's express the complex number we're given in algebraic form.[tex] \\ [/tex]
[tex] \sf z = \dfrac{7 - 8i}{ - 5 + 3i} \\ \\ \\ \diamond \sf Multiply \: both \: the \: numerator \: and \: the \: denominator \: by \: the \: conjugate \: of \: - 5 + 3i. \\ \\ \\ \sf z = \bigg(\frac{7 - 8i }{ - 5 + 3i \: } \bigg) \times \bigg( \frac{ - 5 - 3i}{ - 5 - 3i} \bigg) = \dfrac{(7 - 8i)( - 5 - 3i)}{( - 5 + 3i)( - 5 - 3i)} \\ \\ \\ \diamond \: \sf Expand \: knowing \: that \: (a + b)(c + d) = ac + ad + bc + bd. \\ \\ \\ \\ \sf z = \dfrac{7( - 5) + 7( - 3i) + ( - 8i)( - 5) + ( - 8i)( - 3i)}{( - 5)( - 5) + ( - 5)( - 3i) + 3i( - 5) + 3i ( - 3i)} \\ \\ \\ \sf z = \dfrac{ - 35 - 21i + 40i + 24 {i}^{2} }{25 + 15i - 15i - 9 {i}^{2} } = \dfrac{24 {i}^{2} + 19i - 35 }{25 - 9{i}^{2} } \\ \\ \\ \diamond \sf \: Substitute \: {i}^{2} = - 1. \\ \\ \\ \sf \: z = \dfrac{24( - 1) + 19i - 35}{25 - 9( - 1)} = \dfrac{ - 24 + 19i - 35}{25 - ( - 9)} = \dfrac{ - 59 + 19i}{34} \\ \\ \\ \diamond \: \sf Simplify \: the \: expression. \\ \\ \sf \: z = \dfrac{ - 59 + 19i}{34} = \dfrac{ - 59}{ \: \: 34} + \dfrac{19i}{34} \\ \\ \\ \\ \implies \boxed{ \boxed{ \sf z = - \dfrac{59}{34} + \dfrac{19}{34}i }} [/tex]
[tex] \\ \\ [/tex]
▪️Learn more about the algebraic form of a complex number here:
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Corner Grocery charges $4.80 for 12 sodas. Max's Market charges $5.25 for 15 sodas.
Which store has the best unit price on sodas, and by how much?
Answer:
To do this, just do 12 divided by 4.80 = 2.5 dollars per can at Corner Grocery, and at Max's Market 15 divided by 5.25 = 2.85 per can. So the Corner Grocery has a better unit price by 35 cents.
Thanks for your question.
Answer:
i dont know
Step-by-step explanation:
i dont know
Can anyone help me ASAP!
Answer:
False
Step-by-step explanation:
Make me brainliest
the sum of two numbers is 98. if the larger number is divided by the smaller the quotient is 4 with a remander of 13. Find the two numbers
Answer: x = 81, y = 17
Step-by-step explanation:
x + y = 98
x/y = 4/13/y
x/y = 4y + 13/ y
x = 98 - y
(98 - y) / y = (4y+ 13) / y
Therefore
98 - y = 4y + 13
Collect like terms
-4y - y = 13 - 98
-5y = -85
Divide both sides by-5
y = 17
x = 98 - y
x = 98 - 17
x = 81
The two numbers x and y are 81 and 17 respectively.
What are the Quotients?Quotients are the number that is obtained by dividing one number by another number.
Dividend ÷ Divisor = Quotients
Given that the sum of two numbers is 98.
Let x and y be the two numbers
x + y = 98
Thus, the larger number is divided by the smaller quotient is 4 with a remainder of 13.
x/y = 4/13/y
x/y = 4y + 13/ y
x = 98 - y
(98 - y) / y = (4y+ 13) / y
Therefore,
98 - y = 4y + 13
Collect like terms;
-4y - y = 13 - 98
-5y = -85
Divide both sides by-5;
y = 17
x = 98 - y
x = 98 - 17
x = 81
Therefore, the two numbers x and y are 81 and 17 respectively.
Learn more about the quotient;
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#SPJ2
20% = 0.2 (true or false)
Answer:
TRUE
Step-by-step explanation:
20% is a 5th part of 100% which means that the same part of 1 is 0.2
Answer: its true
Step-by-step explanation: took the test
if 15 baseballs cost $9 how much would 30 baseballs cost
Help please me please
Answer:
5n^3
Step-by-step explanation:
For this type of problem, you can do the numbers and the variables separately and then combine them at the end.
First, lets do the variables:
n^4 has the following factors: n^1, n^2, n^3, n^4
n^3 has the following factors: n^1, n^2, n^3
The greatest common factor is n^3
Now for the numbers.
5 has the following factors: 1,5
30 has the following factors: 1,2,3,5,6,10,15,30
The greatest common factor is 5
Put it all together and the answer is 5n^3
Answer:
the greatest common factor between those is 5n^3
Step-by-step explanation:
So if you factor out 5n^3 you would have,
5n^3(n+ 6)
-16(x+1)=-4(2+4x) solve for x
pls help!
Answer:
No solution
Step-by-step explanation:
[tex] \\ - 16(x + 1) = - 4(2 + 4x)[/tex]
[tex] \\ \mapsto - 16x - 16 = - 8 - 16x[/tex]
[tex] \\ \mapsto - 16 = - 8 - 16x + 16x[/tex]
[tex] \\ \mapsto - 16 = - 8[/tex]
Do not have solution
What does it mean when two things have the same rate?
Answer:
Refer to the explanation for the answer!
Step-by-step explanation:
What does it mean when two things have the same rate?
Having the same rate of something else means it's synchronized or the same. A real world example could be two cars going the same speed, so not only are they going at the same pace, but the two cars have the same rate.
Hope this helped, if you have additional questions let me know!
A person has $20,000 to invest. As the person's financial consultant, you recommend that the money be invested in Treasury bills that yield 3%, Treasury bonds that yield 6%, and
corporate bonds that yield 9%. The person wants to have an annual income of $1170, and the amount invested in corporate bonds must be half that invested in Treasury bills. Find
the amount in each investment.
What is the solution? Select the correct choice below and fill in any answer boxes within your choice
He invested $ 2000 in Treasury bills, $ 1000 in corporate bonds and $ 17000 in Treasury bonds.
Given that a person has $ 20,000 to invest, and as the person's financial consultant, you recommend that the money be invested in Treasury bills that yield 3%, Treasury bonds that yield 6%, and corporate bonds that yield 9%, and the person wants to have an annual income of $ 1170, and the amount invested in corporate bonds must be half that invested in Treasury bills, to find the amount in each investment the following calculation must be performed:
10,000 x 0.03 + 5,000 x 0.09 + 5,000 x 0.06 = 1050 8,000 x 0.03 + 4,000 x 0.09 + 8,000 x 0.06 = 1080 2,000 x 0.03 + 1,000 x 0.09 + 17,000 x 0.06 = 1170
Therefore, he invested $ 2000 in Treasury bills, $ 1000 in corporate bonds and $ 17000 in Treasury bonds.
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Bartley has Five-sevenths of a cup of whole milk and One-seventh of a cup of skim milk. He combines the milk into one container to make a protein shake.
How many cups of milk does Bartley have?
Answer:
Bartley has 50 cups of milk
Step-by-step explanation:
5/7 cups of milk so that will be they answer because your droping it and not hearing it
4(2x+3)+4(3x+2) i need to expand and simplify it
Answer:
8x+12+12x+8=0
20x+20=0
20x=-20
x=-1
Answer:
20
Solve: 2x + 15 = 43 - 5x
Answer:
x = 4
Step-by-step explanation:
2x + 15 = 43 - 5x
2x + 5x = 43 - 15
7x = 28
x = 28/7
x = 4
Answer:
x = 4
Step-by-step explanation:
Step 1: Simplify both sides of the equation
2x +15 = 43 - 5x
2x +15 = 43 + - 5x
2x +15 = - 5x + 43
Step 2: Add 5x to both sides
2x + 15 + 5x= - 5x + 43 + 5x
7x +15 = 43
Step 3: Subtract 15 from both sides.
7x +15 -15 = 43 - 15
7x = 28
Step 4: Divide both sides by 7.
7x/7 = 28/7
Therefore the X = 4
Write how much Julie makes as a rate. What is the unit rate?
Answer:
rate: $12 dollars per hour, 6$ per half hour, etc.
unit rate: $12 per hour
work:
unit rate is how much of per one. 12 per hour is already in unit rates.
Isjfjsjsjdbsbd please sleep is important
Answer:
13 1/2
Step-by-step explanation:
What we do is convert the mixed numbers into improper fractions
1 x 2 + 1 = 3
4 x 2 + 1 = 9
our new fractions are 3/2 and 9/2
multiply 3 x 9 = 27/2
simplify into mixed number = 13 1/2
choose the scenario that could be represented by 5/6
A. five-foot piece of firewood is cut into six equal pieces
B. Six cups of dog food are fed to five dogs equally
C. A five-foot piece of firewood is cut into six equal pieces
D. Six ounces of cereal are shaded equally among five people
Trinity purchase a 2 L bottle of soda from the store how many millimeters of soda did Trinity purchase
Answer:
Final answer: The best deal is the 2 L bottles for $1.79 each. We'll need 12 of them, which will cost us $21.48
Step-by-step explanation:
Hope it's helpful
We need to convert 2L to mL
1L=1000mLNow convert
[tex]\\ \tt\hookrightarrow 2L[/tex]
[tex]\\ \tt\hookrightarrow 2(1000)[/tex]
[tex]\\ \tt\hookrightarrow 2000mL[/tex]
-1+2x=x+3
help assappp
Answer:
4
Step-by-step explanation:
add the 1 to the 3 turns to 2x=x+4, then subtract the 1x to the 2x turns to 1x=4 or x=4
Answer:
4
Step-by-step explanation:
please help with this question
f(n)=2.55+3.75(n), n>0
Answer:
SR= 2.55
GC=3.75
n=?
n rep number of games
SR shoe rental
GC Game cost
f(n)=2.55+3.75n
2.55=3.75n
n=2.55÷3.75
n=0.68
Divide 4.5kg in the ratio 4:5
Answer:
2 Kg and 2.5Kg.
Step-by-step explanation:
Total number of parts = 4 + 5 = 9.
So the required quantities are 4*4.5 / 9 and 5*4.5/9
= 2 and 2.5.
Answer:
2 : 2.5
Step-by-step explanation:
4 : 5 ----> 4x, 5x
4x + 5x = 4.5
9x = 4.5
x = 4.5 / 9
x = 0.5
4x
= 4 x 0.5
= 2
5x
= 5 x 0.5
= 2.5
4 : 5
= 4x : 5x
= 2 : 2.5
someone help me. i don’t understand this lol
Answer:
2
Step-by-step explanation:
the theorum you need for this is c^2 = a^2 + b^2, but because you have sides a and c, you need to work backwards.
Start by isolating b^2 in the equation.
c^2 = a^2 + b^2
-a^2
c^2 - a^2 = b^2
b needs to not be squared, so take the square root of both sides
[tex]b = \sqrt{\sqrt{29}^{2} - 5^{2}[/tex]
Your answer should be 2.
Use the distributive property to remove the parentheses (x - 12) 7
Answer:
6999999
Step-by-step explanation:
Funny Number.
546863 / 57379 in step by step
Answer:
0.1
Step-by-step explanation
57379/546863 is how it should be set
also not sure about the step by step part sorry
Answer:
9 R 30,452
Step-by-step explanation:
are the given lines parallel? Explain your reasoning
Answer:
Yes
Step-by-step explanation:
Because, without the x, it makes them both a horizontal line. Therefore, never intersecting. Meaning, parallel.
Paul brought $24.50 to the art supply store. He bought a brush, a sketchbook, and a paint set. The brush was 1 3 as much as the sketchbook, and the sketchbook cost 1 2 the cost of the paint set. Paul had $2.00 left over after buying these items. What was the cost of each item
Answer:
so do
24.50-13=11.50
11.50-12.00= answer
Step-by-step explanation:
I think so
The amount of snow on the ground increased by 4 inches between 1 p.m. and 6 p.m. What integer represents the amount of snow that fell during those five hours?
Answer:
The snow from each event melts off before the next accumulation and no snow is on the ground at your scheduled time of observation. The total snowfall for that reporting 24-hour day is the sum of the three separate snow squalls, 6.7 inches, even though the snow depth on your board at observation time was zero. Snow often melts as it lands. your welcome!
Someone help jm so confused
Sorry about that.
(21 - 17)² + 3⁴ =
4² + 81 =
16 + 81 =
Answer: 97
Answer:
97
Step-by-step explanation:
(21-17)²+3⁴=4²+81
=16+81
=97
Please help me solve this problem ASAP!
Answer:
angles
Step-by-step explanation:
the angles of these triangles are same
z is equivalent to p
w is equivalent to h
x is equivalent to r
or
Hugo works for the Produce and Pantry grocery store as a bagger. He earns $57.50 for a 5-hour shift. How much does he earn per hour?
Answer:
$11.50
Step-by-step explanation:
57.50 in 5 hours
→ Divide 57.50 by 5
$11.50
Find the slope of the line
Answer:
Step-by-step explanation:
A
