Help please.
Simplify: 2 + 3i / 4 + 2i

Help Please.Simplify: 2 + 3i / 4 + 2i

Answers

Answer 1

Answer:

○ [tex]\displaystyle \frac{7 + 4i}{10}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{2 + 3i}{4 + 2i} → \frac{2 + 3i[4 - 2i]}{4 + 2i[4 - 2i]} = \frac{14 + 8i}{20} = \boxed{\frac{7}{10} + \frac{2}{5}i}[/tex]

When dividing complex numbers, multiply the denominatour and numeratour by the conjugate of the denominatour. Then simply towards the end.

* Here is something you should know:

[tex]\displaystyle \sqrt{-1} = i \\ -1 = i^2 \\ -i = i^3 \\ 1 = i^4\: [every\:multiple\:of\:four][/tex]

I am joyous to assist you at any time.


Related Questions

did i do it correctly if i didnt can u please answer it correctly and tell me how u did it

Answers

Answer:

You have done it wrong.

Step-by-step explanation:

4 3/7 - 5/7 = 3 5/7

We can change the equation to a improper fraction first.

4 3/7 = 4*7+3 = 31/7

31-5 = 26

Therefore the answer is 26/7.

simplify

The answer is equal to 26/7, or 21/7 + 5/7

Which is 3 5/7

Sorry but you did it wrong...

First you gonna make 4[tex]\frac{3}{7}[/tex] become 3[tex]\frac{10}{7}[/tex] ( 4 -> 3 [tex]\frac{7}{7}[/tex] - *you need to make it become the same denominator)

Lets do it:  3[tex]\frac{10}{7}[/tex] - [tex]\frac{5}{7}[/tex] = ...

Because in  [tex]\frac{5}{7}[/tex]  doesn't have a whole number so you will still keep 3

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

Next, you gonna subtract [tex]\frac{10}{7}[/tex] - [tex]\frac{5}{7}[/tex] = [tex]\frac{10-5}{7}[/tex] = [tex]\frac{5}{7}[/tex]

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

SO the answer for 4[tex]\frac{3}{7}[/tex] - [tex]\frac{5}{7}[/tex] is 3[tex]\frac{5}{7}[/tex]

Hope it helps, Studywell!

FACTORIZA COMPLETAMENTE LA SIGUIENTE EXPRESION ALGEBRAICA.
1 - n6 =

Answers

Answer:

-(n -1)(n^2 + n + 1)(n + 1)(n^2 - n + 1).

Step-by-step explanation:

1 - n^6 = (1 - n^3)(1 + n^3)

1 - n^3 = -(n -1)(n^2 + n + 1)  and

1 + n^3 = (n + 1)(n^2 - n + 1)

So Substituting we have:

-(n -1)(n^2 + n + 1)(n + 1)(n^2 - n + 1)

(10-1)(10-2)(10-3)(10-10)

Answers

Answer:

0

Step-by-step explanation:

9 × 8 × 7 × 0

anything that is multiplied by 0 equals to 0

9.8.7.0=0 because a.0=0

Please help fast elementary school all questions

Answers

Write the highlighted digit's place and value.

3. 567; ones place                4. 6,327; thousandth place

5. 9,325; hundredth place    6. 8,281; tenth place

Write each number in standard form.

7. 5,000 + 500 + 3; 5,503     8. 2,000 + 300 + 20 + 9; 2,329

9. 4,000 + 600 + 8; 4,608     9. 9,000 + 300 + 70 + 2; 9,372

11. 1,221

We know Sierra has the same numbers in the thousandth and ones place, so keep does numbers: 1,?2?

It also has two more hundreds and 3 fewer ones place: Take the original number; 1,024 (Make sure you keep the numbers) into a equation; (1024+200)-3. First Add as it's in the ( ), then subtract, 1,221

I hope I've helped!

Answer:

#3. ones place. #4. thousands place.#5. hundreds place. #6. tens place. #7. 5,503. #8. 2,329. #9. 4,608. #10. 9,372.

Step-by-step explanation:

#11.sierras seat number 1,221

55 points. Please help fast. Fastest one (must be correct too) will get brainliest.

Answers

Answer:

Uhh I think some information is missing I am not sure tho

The temperature at 4:00 p.m. was -6 °C, and then it fell by 7 °C. Which expression represents the new temperature? .

Answers

Proteins consist of monomers of glucose bonded together in a variety of ways and can function as energy, enzymes, and transport.

Proteins function as storage, movement, and defense and are diverse due to the arrangement of the nucleic acids.

Here is the histogram of a data distribution. All class widths are 1
What is the median of the distribution?

Answers

Answer:

it is d

Step-by-step explanation:

thank me later yung bloods

math geometry (10 points)

Answers

Answer:

semoga jawapan ini dapat membantu

A number is between 17 and 22. It has prime factors of 2​, and 5. What is the​ number?

Answers

Answer:

20

Step-by-step explanation:

20 fits all of the requirements.

It is between 17 and 22.

2 and 5 are two of its factors.

I hope this helps!

pls ❤ and mark brainliest pls!

Answer:

20

....................

express each of the following in standard form 0.0 0 0 0 0 0 0 0 0 2 2 1​

Answers

answer= 2.21 x 10^-10

c = 8 π a b will give brainliest and 30 points

Answers

Answer:

2nd option

Step-by-step explanation:

Given

c = 8πab ( isolate a by dividing both sides by 8πb

[tex]\frac{c}{8\pi b}[/tex] = a

When is ignorance delightful

Answers

IKWKWMWMWM EXACTLYYYYYY

Answer:

Ignorance, or a lack of knowledge, isn't usually viewed as a good thing. However, there may be situations when you're happier not knowing the truth. A common expression used to describe these situations is “Ignorance is bliss.” This phrase is an idiom, which is means that it isn't meant to be taken literally.

I am super late

c. Draw the rotation of Pentagon ABCDE around C clockwise by an angle of 150
degrees. Tracing paper and a protractor may be useful.
E
D
B
-

Answers

The answer is b ur welcome

divide 6q by q please solve this and help me to get out of this​

Answers

Step-by-step explanation:

the answer is 6

please mark me brainliest

Answer:

[tex] \frac{6q}{q} \\ \frac{6 \times q}{q} \\ when \: q \: is \: divided \: by \: q \: then \: the \: remainder \: is \: 1 \\ 6 \times 1 \\ 6[/tex]

Natasha's rectangle measures 4 1/2 units by 2 1/4 units. What is its area?

Answers

Answer:

Answer: 49/6units^{2}49/6units

2

Step-by-step explanation:

You can convert from mixed number to fractions as following:

2 1/3=((2*3)+1)/3=7/3 units

3 1/2=((3*2)+1)/2=7/2 units

Then you can calculate the area of the rectangle as you can see below:

\begin{gathered}Area=lenght*width\\Area=7/2units*7/3units\\Area=49/6units^{2}\end{gathered}

Area=lenght∗width

Area=7/2units∗7/3units

Area=49/6units

2

Answer:

[tex]10\frac{1}{8}[/tex]

Step-by-step explanation:

→ Multiply the fractions together

[tex]4\frac{1}{2} *2\frac{1}{4}[/tex]

→ Convert to improper fractions

[tex]\frac{9}{2} *\frac{9}{4}[/tex]

→ Multiply across

[tex]\frac{81}{8}[/tex]

→ Convert back to mixed number

[tex]10\frac{1}{8}[/tex]

oh my god help plssss ima rage

Answers

Answer:

d

Step-by-step explanation:

Given h(x) = 4x – 5, solve for a when h(x) = 7.

Answers

h(x)=4x-5

[tex]\\ \sf\longmapsto h(7)[/tex]

[tex]\\ \sf\longmapsto 4(7)-5[/tex]

[tex]\\ \sf\longmapsto 28-5[/tex]

[tex]\\ \sf\longmapsto 23[/tex]

Answer:

23

Step-by-step explanation:

h(7)= 4(7) - 5

h(7)= 28 - 5

h(7)= 23

Prove this

1-tan^2x/1+tan^2x=cos^2x-sin^2x

Answers

Answer:

see explanation

Step-by-step explanation:

Using the identity

tan x = [tex]\frac{sinx}{cosx}[/tex]

Consider the left side

[tex]\frac{1-tan^2x}{1+tan^2x}[/tex]

= [tex]\frac{1-\frac{sin^2x}{cos^2x} }{1+\frac{sin^2x}{cos^2x} }[/tex] ( multiply numerator and denominator by cos²x to clear fractions

= [tex]\frac{cos^2x-sin^2x}{cos^2x+sin^2x}[/tex] ← ( cos²x + sin²x = 1 ]

= cos²x - sin²x

= right side , thus proven

ANY ONE HELP ME ASNWER THIS QUESTION

Find the value of 'x' in the following diagram:
the number 2 answer the 2nd one

Answers

Answer:

Question 2

180=2x+3x

180=5x

36=x

Answer:

[tex]than k \: you[/tex]

Find the probability of “landing” in the shaded region of the figures below. Round your answer to the nearest hundredth.
3. Square with side length 40 ft

Answers

Answer:

Area of the square:

A = a² = 40² = 1600 ft²

Area of the circle:

A = πr² = 3.14*(40/2)² = 1256 ft²

Probability of landing in the shaded region:

P = 1256/1600 = 0.785 or 78.5%

Answer:

78.5%

Step-by-step explanation:

We can find the area of both shapes then divide to find the probability.

Square area:

40 * 40 = 1600ft²

Circle area with diameter [ 1/4πd² ]:

1/4π(40)²

1/4π(1600)

0.785(1600)

1,256

Now divide both areas to find the probability.

1256/1600 = 0.785

0.785 * 100% = 78.5%

Best of Luck!

please please help me it's for my homework ​

Answers

Answer:

6/25

Step-by-step explanation:

.24 = 24/100 = 6/25

Answer:

6/25

Step-by-step explanation:

step 1 The decimal number = 0.24

step 2 Write it as a fraction

0.24/1

step 3 Multiply 100 to both numerator & denominator

(0.24 x 100)/(1 x 100) = 24/100

It can be written as 24% = 24/100 or 24/100

step 4 To simplify 24/100 to its lowest terms, find LCM (Least Common Multiple) for 24 & 100.

4 is the LCM for 24 & 100

step 5 divide numerator & denominator by 4

24/100 = (24 / 4) / (100 / 4)

= 6/25

6/25 is a simplest fraction for the decimal point number 0.24

Solve. 4x + 3 = 47
A x= 11 B x=40 C x=44 D x=50

Answers

Answer:

x=11

Step-by-step explanation:

The answer is A.) x=11

I own the collector’s edition of my favorite Pokemon card. It used to be worth $120 USD. Now it is worth $150 USD.

What is the percent change?

Answers

Answer:

By 25%

Step-by-step explanation:

150-120=30 30/120=1/4 1/4=25%

Check:

120x.25=30 30+120=150

Hope this helps

Whats ur favortie pokemon? (:

Please give answer to the problem.

Answers

y = x - 4 so if x = -3 then y = -3 - 4 = -7

100 points

Kala has scored 18, 22, 19, and 26 points in her four basketball games so far. How many
points does she need to score in her next game so that her average (mean) is 21 points per
game?

Answers

Answer:

Kala must score 20 points in her fifth game.

Step-by-step explanation:

The mean or average of a set is given by:

[tex]\displaystyle \overline{x} = \frac{\text{sum of data values}}{\text{number of data values}}[/tex]

(Note: the symbol used to denote the mean is known as "x-bar.")

We want to find the points (let the unknown value be a) Kala needs to score in her fifth game such that her average score is 21 points per game.

In other words, her total score so far plus a all over five (five games in total) must equal 21:

[tex]\displaystyle (21) = \frac{(18) + (22) + (19) + (26) + a}{5}[/tex]

Solve for a. Multiply and combine like terms:

[tex]\displaystyle 105 = 85 + a[/tex]

Subtract. Hence:

[tex]a = 20 \text{ points}[/tex]

In conclusion, Kala must score 20 points in her fifth game.

Answer:

Answer :-

We know that

Average = Sum of observation/Total observation

Let the unknown observation be x

18 + 22 + 19 + 26 + x/5 = 21

85 + x/5 = 21

85 + x = 21 × 5

85 + x = 105

x = 105 - 85

x = 20

URGENT ! HELP ME I WILL MARK BRAINLIEST !!

please faster !!!!​

Answers

Step-by-step explanation:

230m...................

Answer: so the answer would actually b

Step-by-step explanation:

please help me I am stuck on this question​

Answers

Answer:

(a) $3.00

(b)(i) $33.00

(b)(ii) $322.50

Step-by-step explanation:

(a)

100% = $20.00

1% = 100%/100 = 20/100 = $0.20

15% = 1%×15 = 0.2×15 = $3.00

so, he actually has to pay $20 + $3 = $23 per toaster.

or shorter and direct, since we calculate the extra 15% based on the original 100%, we can say he has to pay 115% of the basic price.

115% = 0.2×115 or = 100%×1.15 = 20×1.15

0.2 × 115 = $23

20 × 1.15 = $23

so, you can see the several ways to get to the result.

in any case, the profit is $26-$23 = $3 per toaster.

(b)(i)

100% new price = 100% old price + 20% = 120% old price

or 100% old price × 1.2

100% new price per toaster = 20×1.2 = $24.00

the new tax is increased TO 25% (not by 25%) be careful to see that detail.

so, we need to add 25% of the new price.

125% new price = 24×1.25 = $30.00

so, in order to make again $3 profit, the customer has to pay now $30+$3 = $33.00

(b)(ii)

100% (b)(i) selling price = $33.00

30% more means 130% of that, or 1.3×100%

33×1.3 = $42.90

so, the profit per toaster is now 42.90 - 30 = $12.90

when selling 25 of these toasters the profit is then

25×12.90 = $322.50

Alvin's age is two times Elga's age. The sum of their ages is 81 . What is Elga's age?

Answers

Answer:

Elga is 27 years old

Step-by-step explanation:

       AGE 27

Alvin 2x

Elga  x

x+2x = 81

81=3x

81/3=x

x=27

Hope this helps! (:

Answer:

Elga's age is 27.

Step-by-step explanation:

x + 2x = 813x ÷ 3 = 81 ÷ 3x = 27Checking:27 + 2(27) = 8181 = 81

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Ele:
2.
Find the sum of the digits of each multiple of 9 below.
Sum of digits
9
1 + 8 = 9
9.1 = 9
9.2 = 18
9.3 = 27
9.4 = 36
9.5 = 45
9.6 = 54
9.7 = 63
9.8 = 72
9.9 = 81
Describe a pattern. (Do you think it will continue?)

Answers

Answer:

The pattern is that, every time a 9 is added. This pattern continuous forever.

Step-by-step explanation:

9 X 1 = 9

9 X 2 = 18 (9+9)

9 X 3 = 27 (9+9+9)

Etc.

Which option is the correct interpretation of this numerical expression?
55 ÷ 5 − 4

the quotient of 55 divided by 5, decreased by 4

four subtracted from the product of 55 and 5

five less than the quotient of 55 divided by 4

fifty-five divided by the difference of 5 and 4

Answers

Answer:

7

Step-by-step explanation:

bc 11×5=55 so you divide it and its 11-4=7 :)

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