1/(2+i)²

Solve this question....​

Answers

Answer 1

[tex]\large\underline{\sf{Solution-}}[/tex]

Given complex number is

[tex]\rm \longmapsto\:\dfrac{1}{ {(2 + i)}^{2} } [/tex]

[tex]\rm \:  =  \: \dfrac{1}{4 + {i}^{2} + 2 \times 2 \times i} [/tex]

[tex]\rm \:  =  \: \dfrac{1}{4 - 1 + 4i} [/tex]

[tex]\rm \:  =  \: \dfrac{1}{3+ 4i} [/tex]

[tex]\rm \:  =  \: \dfrac{1}{3+ 4i} \times \dfrac{3 - 4i}{3 - 4i} [/tex]

[tex]\rm \:  =  \: \dfrac{3 - 4i}{ {3}^{2} - {(4i)}^{2} } [/tex]

[tex]\rm \:  =  \: \dfrac{3 - 4i}{9 -16 {i}^{2} } [/tex]

We know,

[tex] \rm \longmapsto\:\tt{ {i}^{2} \: = \: - \: 1 \: } \\ [/tex]

So, using this, we get

[tex]\rm \:  =  \: \dfrac{3 - 4i}{9 -16( - 1)} [/tex]

[tex]\rm \:  =  \: \dfrac{3 - 4i}{9 + 16} [/tex]

[tex]\rm \:  =  \: \dfrac{3 - 4i}{25} [/tex]

[tex]\rm \:  =  \: \dfrac{3}{25} - \dfrac{4}{25}i[/tex]


Related Questions

Solve for x.

2x/3 +1=3

O x =6
O x =3
O x = 1 1/3
O x = 2 2/3

Answers

Answer:

3......................

Answer:

X=3!

Let's solve your equation step-by-step.

Step 1: Simplify both sides of the equation.  

Step 2: Subtract 1 from both sides.

Step 3: Multiply both sides by 3/2.

Answer:

x=3

Shaq painted 600 portraits in 8 hours at that rate how many portraits would he paint in 4 minutes?

Answers

Answer: In 4 minutes he will make 5 portraits

Step-by-step explanation:

[tex]\large \boldsymbol{} 600p-8h=480 min \\\\ x \ p-4 min \\\\ x=\dfrac{600\cdot 4}{480} =\dfrac{2400}{480} =5 \ portraits \\\\ \rm Answer : 5[/tex]

Hello! I need help with this question

Answers

Each min is =0.75$
So 5$ can talk 5$/0.75$ =6.6667 min
First option

The Elsie Dairy uses a machine that fills 28 cartons of milk an hour. How many will be filled in 6.5 hours?

Answers

Answer:

About 182 cartons will be filled in 6.5 hours.

Step-by-step explanation:

Multiply 6.5 by 28 to get 182

Answer:

The answer is 182

Step-by-step explanation:

28 x 6.5 = 182. if the machine fills 28 cartoons in a hour and you leave it running for 6.5 or 6 hours and 30 minutes that will be 182 cartoons filled in that amount of time.

what is 2/4 added to 1/3?​

Answers

5/6. fine the common factor of both 4 and 3 and multiple and than simplify.

find the product of ​

Answers

what’s the questionnnn
1/2 × 2/3 × 3/4 × 4/5
=1/5
Please mark brainliest

The picture needs to be answered.

Answers

Answer:

if 3 children go to the water park, 4 adults can go: TRUE

if 6 children go to the water park 3 adjults can go: FALSE

no adults, 6 children: TRUE (even 9 children can go)

no children, 6 adults: TRUE

10x is indeed the cost of the children

15y is indeed the cost of the adults

Help ASAP!!! ILL GOVE BRAINLIEST IF YOU GET IT RIGHT!

Answers

Step-by-step explanation:

I am not sure but i think it is D or E (last 2 choices)

Sorry if wrong

Isabella and her brother, Santiago, want to make their grandma's famous fruit salad, but they can't remember how to make the honey-lime dressing. They decide to make two versions with different amounts of sweet honey and tangy lime, then compare them. Isabella mixes 4 tablespoons of honey and 2 tablespoons of lime juice. Santiago mixes 5 tablespoons of honey and 4 tablespoons of lime juice. Whose dressing is sweeter?

Answers

Answer:

Isabella

Step-by-step explanation:

4:2, is Isabella's ratio of honey:lime.

5:4, is Santiagio's ratio of honey:lime.

Therefore, Isabella has 6 equal parts over all and 4/6 of those parts are honey.

Santiago, has 9 equal parts, so he has 5/9 parts of honey.

Next is to make the denominators the same:

That would make the denominators 54 and then you just multiply the opposite denominator to the numerator:

5/9=36/54

4/6=30/54.

This means that Isabella's dressing is sweeter.

what are the two possible names for the line between a reflection

Answers

Answer:

Line m, because if you put a mirror on m, one figure will be truly reflected in another

line m.. it will be reflected with a mirror

I really need help finding the solution!!

Answers

Answer:

-0.5 is not a solution

2 is a solution

Step-by-step explanation:

To check if something is a solution of the equation, you need to substitute the value in place of the variable

15 + 2y = -12 - 4y

15 + 2(-0.5) = -12 - 4(-0.5)

15 - 1 = -12 + 2

14 ≠ -10 ∴ -0.5 is not a solution

5 - 2(3x + 5) = 3 - 10x

5 - 2[3(2) + 5] = 3 - 10(2)

5 - 2(6 + 5) = 3 - 10(2)

5 - 12 - 10 = 3 - 120

-17 = -17 ∴ 2 is a solution

c. Point B (-3, -4) is also on the circle. Verify algebraically whether triangle OAB is a
right-angle triangle.

Answers

Answer:

89

Step-by-step explanation:

don't use this awnser its wrong

Mother bought 3 cans of sardines at ₱17.80 each, 5 cans of milk at ₱38.85 each, 3kg sugar at ₱60.50 each, and 2 cans of corn beef at ₱78.85 each. Find the total amount bought. If she paid ₱500 bill, find her change.​

Answers

Step-by-step explanation:

Total amount is:

3*17.80 + 5*38.85 + 3*60.50 + 2*78.85 = 586.85

If the numbers are correct ₱500 won't be enough as the total amount exceeds it.

Question:

Mother bought 3 cans of sardines at ₱17.80 each, 5 cans of milk at ₱38.85 each, 3kg sugar at ₱60.50 each, and 2 cans of corn beef at ₱78.85 each. Find the total amount bought. If she paid ₱500 bill, find her change.

Statement:

Mother bought 3 cans of sardines at ₱17.80 each, 5 cans of milk at ₱38.85 each, 3kg sugar at ₱60.50 each, and 2 cans of corn beef at ₱78.85 each.

Solution:

The total amount for which she had brought the items

= ₱ (3×17.80 + 5×38.85 + 3×60.50 + 2×78.85)

= ₱ (53.40 + 194.25 + 181.50 + 157.70)

= ₱ 586.85

Answer:

The total amount for which she had brought the items is ₱ 586.85.

I cannot solve the second part of the sum because the amount exceeds ₱ 500.

Hope it helps

Simplify
10-2
103
-100,000
*
1
10
1
10
100,000
RETRY

Answers

Answer:

100,000

Step-by-step explanation:

[tex] (\dfrac{10^{-2}}{10^3})^{-1} = [/tex]

When you divide powers with the same base, subtract the exponents.

[tex] = (10^{-2 - 3})^{-1} [/tex]

[tex] = (10^{-5})^{-1} [/tex]

To raise a power to a power, multiply the exponents.

[tex] = 10^{-5 \times (-1)} [/tex]

[tex] = 10^5 [/tex]

[tex] = 100,000 [/tex]

HELP ME PLEASE PLEASE PLEASE​

Answers

Answer:

#1)  3 different roots, total 6#2) 3 different roots, total 9#3) 3 different roots, total 4

Step-by-step explanation:

#1

The roots are:

x - 3 = 0 ⇒ x = 3, multiplicity 2x + 1 = 0 ⇒ x = -1, multiplicity 32x + 5 = 0 ⇒ x = -2.5#2

The roots are:

x = 0, multiplicity 3x + 2 = 0 ⇒ x = -2x - 4 = 0 ⇒ x = 4, multiplicity 5#3

The roots are:

x² - 1 = 0 ⇒ (x + 1)(x - 1) = 0 ⇒ x = -1, x = 1x² + 4x + 4 = 0 ⇒ (x + 2)² = 0 ⇒ x + 2 = 0 ⇒ x = -1, multiplicity 2

Please help me on this it’s due

Answers

Answer:  5 cakes

================================================

Explanation:

Let's start off converting the mixed number 12 & 1/4 to an improper fraction.

[tex]a \frac{b}{c} = \frac{a*c+b}{c}\\\\12 \frac{1}{4} = \frac{12*4+1}{4}\\\\12 \frac{1}{4} = \frac{49}{4}\\\\[/tex]

Do the same for the other mixed number 2 & 1/3.

[tex]a \frac{b}{c} = \frac{a*c+b}{c}\\\\2 \frac{1}{3} = \frac{2*3+1}{3}\\\\2 \frac{1}{3} = \frac{7}{3}\\\\[/tex]

-----------------------

From here, we divide the two fractions. I converted them to improper fractions to make the division process easier.

[tex]\frac{49}{4} \div \frac{7}{3} = \frac{49}{4} \times \frac{3}{7}\\\\\frac{49}{4} \div \frac{7}{3} = \frac{49\times 3}{4\times 7}\\\\\frac{49}{4} \div \frac{7}{3} = \frac{7\times 7\times 3}{4\times 7}\\\\\frac{49}{4} \div \frac{7}{3} = \frac{7\times 3}{4}\\\\\frac{49}{4} \div \frac{7}{3} = \frac{21}{4}\\\\[/tex]

The last step is to convert that result to a mixed number.

[tex]\frac{21}{4} = \frac{4*5+1}{4}\\\\\frac{21}{4} = \frac{4*5}{4}+\frac{1}{4}\\\\\frac{21}{4} = 4+\frac{1}{4}\\\\\frac{21}{4} = 5 \frac{1}{4}\\\\[/tex]

Note that 21/4 = 5.25 and 1/4 = 0.25 to help check the answer.

-----------------------

Therefore, she can make 5 cakes. The fractional portion 1/4 is ignored since we're only considering whole cakes rather than partial ones.

write each equation in slope-intercept form. underline the slope and circle the y-intercept in each equation 5x+3y=30
The slope - intercept form is: ___

Answers

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]y = \underline{-\frac{5}{3}}x + \boxed{10}[/tex]

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\text{Converting to Slope-Intercept Form:}\\5x + 3y = 30\\\rule{150}{0.5}\\\rightarrow 5x - 5x + 3y = 30 - 5x\\\\\rightarrow 3y = 30-5x\\\\\rightarrow\frac{3y=30-5x}{3}\\\\\rightarrow y = 10 -\frac{5}{3}x\\\\\rightarrow \boxed{y = -\frac{5}{3}x + 10}[/tex]

⸻⸻⸻⸻

[tex]\text{General Slope-Intercept Formula:}\\y = mx + b\\\rule{150}{0.5}\\$\bullet \text{ }m -\text{Slope}\\$\bullet \text{ }b -\text{Y-Intercept}\\\rule{150}{0.5}\\\text{In the given equation, the slope would be } -\frac{5}{3} \text{ and the y-intercept would be } 10.[/tex]

⸻⸻⸻⸻

[tex]y = \underline{-\frac{5}{3}}x + \boxed{10}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Given g(x)=-x-2 find g(-3)

Answers

Answer:

g(-3)=1

Step-by-step explanation:

substitude x=-3

g(-3)=-(-3)-2

=1

Answer:

g(-3) = 1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Functions

Function Notation

Step-by-step explanation:

Step 1: Define

Identify

g(x) = -x - 2

Step 2: Evaluate

Substitute in x [Function g(x)]:                                                                         g(-3) = -(-3) - 2Simplify:                                                                                                             g(-3) = 3 - 2Subtract:                                                                                                            g(-3) = 1

do 12,16, and 20 make a right triangle

Answers

Answer:

so yes it does :)

Step-by-step explanation:

There is a fourth category of triangles in which one of interior angles is of 90∘ . It is called right triangle. 1) 12,16,20 : 202=162+122 : True, hence right triangle

I need help y’all pls I will give brainliest

Answers

Answer: (-2,-2)

Step-by-step explanation:

Start at finding the y-intercept(-3) then do rise over run with -2x

Rise over run is count up/down then left/right

In which part of the graph is the distance from home constant?
Distance from home
Time
A. 4
B. 3
C. 1
D. 2

Answers

Step-by-step explanation:

the answer is A. 4

as a horizontal line

The Answer is 4
——————————

Will give brainliest if correct
Find the slope:
15. (4, 3); (-1, 10)
16. (3, -5); (2, -5)
17. (-5, 2); (-5, 3)

Answers

Answer:

15) Slope (m) = -7/5

16) Slope (m) = 0

17) Slope (m) = 1/0 (It's an undefined slope, in other words it's just a vertical line)

Step-by-step explanation:

Use this formula for each, to find slope⤵⤵⤵

[tex] \frac{y {2} - y1}{x2 - x1} [/tex]

15) ⤵

[tex] \frac{10 - 3}{ - 1 - 4} = \frac{7}{ - 5} = - \frac{7}{5} [/tex]

16) ⤵

[tex]\frac{ - 5 - ( - 5)} {2 - 3} = \frac{0}{ - 1} = 0[/tex]

17) ⤵

[tex] \frac{ 3 - 2}{ - 5 - ( - 5)} = \frac{1}{0} [/tex]

Hope this helps :)

A 24 foot tall streetlight casts a shadow that is 18 feet long. How long of a shadow is cast by a nearby parking meter post that is 4 feet high?

WILL MARK BRAINLIEST for whoever answers in less than 5 minutes

Answers

Answer: A  streetlight casts a shadow 15 feet long. At the same time, a 18-foot flag pole casts a shadow 10 feet long. How tall is the tree? | Socratic A tree casts a shadow 15 feet long.

I really don’t know to be honest

Use the definition f(a) = lim x->a f(x) - f(a)/(x-a) to find the derivative of the given function at the indicated point.2) F(x) =-8 -×2, a = 2. A.) 2 B.) -2 c.) -4 d.)4

Answers

Answer:

B

Step-by-step explanation: HOPE IT HELP

i’m just stuck on #6, is it d or c???

Answers

It’s D because the angles are found in the same relative position on different intersections

Which method used to determine numbers of bacteria in a sample involves the preparation of a series of dilutions of the sample in sterile water, adding measured volumes of each dilution to melted nutrient agar plates, making pour plates, incubating, counting colonies, and multiplying colony counts by dilution factors to determine the number of bacteria in the sample

Answers

Answer:To obtain a readily counted and statistically accurate number of bacteria. When performing a standard plate count using the pour plate method, the dilutions are first made, and then measured aliquots of each dilution are cultured.

Step-by-step explanation:

Please answer my question
12 points will be given
Who wants to be my friend?
Put all your names in the answers box or in the comments

Answers

Answer:

yes

Step-by-step explanation:

i like points lol

Ed is 7 years older than Ted. Ed's age is also 3/2 times Ted's age. How old areTed and Ed.

Answers

14, 28 I think:) sorry if not

The length of a rectangle is 2x + 6. Its width is 52. Find the value of ac if the perimeter is 138m².

Answers

Answer:

ac = 18.5

Step-by-step explanation:

perimeter of a rectangle =  [tex]2(l+b)[/tex]

= 138m^2= 2(2x + 6 ) + 52

= 4x + 12 + 52 = 138  

= 4x + 64 = 138

= 4x = 138 - 64

= 4x = 74

= x =  74/4

= x = 18.5

Solve this equation. 3(x−9)>3x+6

Answers

Answer:

No solution

Step-by-step explanation:

There are no values of x that make the inequality true.

Other Questions
Why is sustainable use of natural resources important? Which of the following would require more energy to heat it from 10C to 20C? a. 200 kg of water b. 200 kg of aluminum C. 100 kg of steel 1240 at 8% compounded annually for 3 years Find the area I will make you Brainliest (show working) An amoeba that lives in salt water does not have a contractile vacuole to do so. Explain observations. Mercury is one of only two elements that are liquid at room temperature. Mercury is nonliquid fortemperatures less than -38.0F or greater than 673.8F. Write a compound inequality for the temperaturesat which mercury is nonliquid. Control of Hawaii contributed to the powers of the United States because the islands Zhanae Gregory bought a total of 25 books and CDs during a yard sale for a total of $65.50. If books cost $1.50 each and CDs cost $5 each, how many books did she buy? Aggressive debridement should be avoided in which of the following typesof wounds that presents with necrosis? The sum of twice a number and 6 You are at the doctor for your yearly physical, and she warns you that eating too much junk food can affect the way your genes express themselves, and that these changes can be passed on to your future children. Which concept is your doctor warning you about? A person plans to drive across country 1,798 miles. At what speed would they have to drive in order to drive no more than 30 hours? Which equation shows the quadratie formula used correctly to solve 7x? = 9+X for x? What are the functions of political system? Plz plz help fast I will mark Brainlyist What was the charter of 1732 rules about land ownership Which of the following is a true statement?Growth cycles only happen to reptiles.Growth cycles happen to all animals.Growth cycles only happen to birds.Growth cycles only happen to mammals. An atom that has twelve protons in its nucleus has an atomic number of:241312none of the above young goodman brown audience with five or six little ones living or en in health and spirit, the wornout sh woman who would reproach us for tryir will save her from giving birth to any more ba chaps to disease and death? It is to make such knowledge legally and medica land that in November 1921 we formed the Ame growing and extending itself across this contine Japan, China and India. Give 3 of Margaret Sanger's Main Points