Perform the indicated operation and express the result as a simplified complex number in the form a+bi. Do not put any spaces between your characters. If your answer includes a number that is not an integer type it as a decimal rounded to the nearest hundredth.
(3+4i)/(2-i)
simplifies to a+bi where:

A=

B=

Answers

Answer 1

9514 1404 393

Answer:

  0.40+2.20i

Step-by-step explanation:

To clear the denominator of its imaginary part, multiply numerator and denominator by the conjugate of the denominator.

  [tex]\dfrac{3+4i}{2-i}=\dfrac{(3+4i)(2+i)}{(2-i)(2+i)}=\dfrac{6-4+3i+8i}{4+1}=\dfrac{2+11i}{5}\\\\=\boxed{0.40+2.2i}[/tex]

_____

Additional comment

This "multiply by the conjugate" is also used to clear radicals from the denominator. It takes advantage of the factoring of the difference of squares:

  (a -b)(a +b) = a² -b²


Related Questions

Can you please solve this please and thank you.

Answers

Answer:

The answer is 3

Step-by-step explanation:

It’s 3 because with dilation your multiplying points to make a shape bigger, so multiply all the numbers by 3 and when you do that you woulda gotten what’s shown in B

The answer is 3. The images side divided by the pre-images side is your scale factor.

12/4 = 3
6/2 = 3

Not very good at math guys I really need to pass my Highschool test pls help

Answers

Answer:

5 $3.00

Step-by-step explanation:

For every 5 apples, the cost is $3.00

Carlos took a total of 8 quizzes over the course of 4
weeks. After attending 7 weeks of school this
quarter, how many quizzes will Pancho have taken in
total?
Help,no links

Answers

Answer:

the answer is 14

Step-by-step

multiply 2x7

Can someone help me with this? (Do not upload through file only text please!)

Answers

Answer:

-6

Step-by-step explanation:

f(0) =  5(0) -6

f(0) = -6

Kayla drives her new car to work every day. It uses 1 3/5 gallons of gas for each round trip. How many round trips to work can Kayla drive on a 16 gallon full tank of gas? The trail length is 15 5/6

Answers

Answer:

10

Step-by-step explanation:

1. The expression 2p - 15 represents the number of lilies left in the zoo's garden after a storm. If p = 223, how many lilies are left in the garden after the storm? 431 lilies 223 lilies 193 lilies 208 lilies​

Answers

2(223)-15
446-15=431lilies

Use a number line to add or subtract.
3−(-1)=

Answers

Answer:

4

Step-by-step explanation:

rule 1 positive + positive= positive

rule 2 negative plus negative = negative

Write a mathematical question that explains the following sentence:

two more than triple a number is fourteen

Answers

two more than triple a number is fourteen might be 2×7=14

Helppp!! I cant get this wrong lol

Answers

Answer:

x = 2

y = -7

Step-by-step explanation:

First, we see that all the terms in the first equation can be divided by 7:

-x + y = - 9

Then we solve for x by adding adding x and 9 to both sides:

-x + x + y + 9 = -9 + 9 + x

it cancels out to:

y + 9 = x

Now, replace x in the second equation with (y + 9):

28(y + 9) - y = 63

Now simplify:

28(y) + 28(9) - y = 63

27y + 252 = 63

27y = 63 - 252

27y = -189

y = -7

Plug in the value for y in the equation for x:

y + 9 = x

-7 + 9 = x

x = 2

Answer:

-7x +7y = -63(i)

28x -y = 63 (ii)

Divide eq(i) by 7

-x + y = -9 (iii)

28x -y= 63 (ii)

Add (iii) and ii

-x + y = -9

28x - y = 63

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

-x +28x +0 = -9 +63

27x = 54

●x = 2

Put x=2 in any eq..

Lets put in eq[i]

-7 (2) + 7y =-63

-14 + 7y = -63

7y = -63 +14

7y=49

●y=7

BRAINLIST PLS

what is the probability that a tabby is chosen as the second kitten when a black kitten was chosen as the first

Answers

0.5/1 it could be 50%

Angles on a line add up to 180. So what is x?

Answers

Answer:

x=121

Step-by-step explanation:

360_304=56180_115=6565+56=121x=121

Answer:

x = 121°

Step-by-step explanation:

180 - 115 = 65°

The angle beside 115° is 65°.

A full circle is 360° so

360 - 304 = 56°

Add the two angles

65 + 56 = 121°

Subtract it to 180° to find the other angle

180 - 121 = 59°

Now subtract again to 180° to find the angle in the other side

180 - 59 = 121°

circle math problem,, area

Answers

Answer:

(E). (33/2)π + 18  

Step-by-step explanation:

The reflex angle = 360 - 30 = 330 degrees.

Length of the curved part = (330/360) * 2π*9 = 33π/2.

The length of the straight lines = 9 + 9 = 18

So the required perimeter = 18 + 33π/2

Awnser this for brainliest

Answers

The distance from the sun is around 2,795,200,200 miles
Distance traveled in one complete orbit of the sun (one “year”) would be around 17,562,300,000 miles
hope this helps

i started some of it but i’m really confused with the rest. does anyone know how to do this?

Answers

Answer:

see below

Step-by-step explanation:

You're doing well!  The parts of the table you've done are correct.

For x = 1, you switch to the second part of the function rule (because that part says to use it if [tex]x \ge 1[/tex].

x =1 :   6 - 2(1) = 4   (1, 4)

x = 2:  6 - 2(2) = 2   (2, 2)

x = 3:  6 - 2(3) = 0   (3, 0)

x = 4:  6 - 2(4) = -2  (4, -2)

Each of the parts of the function rule graph as pieces of straight lines.  The first part will be a straight line through points (-4, 1), (-3, 0), (-2, 1), (0, 3) but that part of the graph stops at point (1, 4).  Point (1, 4) is on BOTH parts of the graph, so the two lines connect at that point.

Answer:

Step-by-step explanation:

Solve for x, then find each angle measure

Answers

(4x-22)+(10x-4)+(x+11)=180
x=13

Answer:

x=13

Q=30

P=126

R=24

Step-by-step explanation:

To find x put them all into an equation like this:

(4x-22)+(10x-4)+(x+11)=180 (we get 180 because all three angles of any triangle always equal 180)

calculate and you'll get x=13.

then to find each angle just put 13 in place of x

4(13)-22=30

10(13)-4=126

(13)+11=24

convert
d) 14 yd² to ft²
e) 5.4 cm² to mm²​

Answers

Answer:

14 yd²= 126 ft²

5.4 cm² = 540 mm²​

Use the information given in the figure to find the length SU.
If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.

Answers

Answer:

We'll calculate ru:

RU^2 = 65^2 - 52^2

RU^2 = 1,521

RU = 39

SU^2 = 89^2 -39^2

SU^2 = 7,921 - 1,521

SU^2 = 6,400

SU = 80

Step-by-step explanation:

Examine the linear relationships.

Linear equation A: y=45x
Linear equation B is represented by this graph.


A line that passes through points (0, 2) and (5, 4).

© 2017 StrongMind. Created using GeoGebra.


Which statement is entirely correct?

Equation A has a steeper slope, because 45 is greater than 25.Equation A has a steeper slope, because 4 fifths is greater than

Equation B has a steeper slope, because 45 is greater than 25.Equation B has a steeper slope, because 4 fifths is greater than

Equation A has a steeper slope, because 52 is greater than 45.Equation A has a steeper slope, because 5 halves is greater than

Equation B has a steeper slope, because 52 is greater than 45.

Answers

Using linear functions, it is found that the correct option is:

Equation A has a steeper slope, because [tex]\frac{4}{5}[/tex] is greater than [tex]\frac{2}{5}[/tex].

A linear function has the following format:

[tex]y = ax + b[/tex]

In which:

a is the slope, which is the rate of change.The higher the slope, the steeper the function is:

Linear equation A is given by:

[tex]y = \frac{4}{5}x[/tex]

Linear equation B passes through points (0, 2) and (5, 4). Since the slope between two points is given by change in y divided by change in x, we have that:

[tex]m = \frac{4 - 2}{5 - 0} = \frac{2}{5}[/tex]

Equation A has a higher slope, hence, it is steeper, and the correct option is:

Equation A has a steeper slope, because [tex]\frac{4}{5}[/tex] is greater than [tex]\frac{2}{5}[/tex].

A similar problem is given at https://brainly.com/question/20386726

A rectangle has one side of 10cm. How fast is the area of the rectangle changing at the instant when the other side is 12 cm and increasing at 3cm per minute

Answers

10x12 = 120
10x15 = 150
10x18 = 180 and so on.
The answer is that the area of the rectangle increase by 30 cm every minute!

30 is the area of the rectangle changing at the instant when the other side is 12 cm and increasing at 3cm per minute

What is Area of Rectangle?

The area of Rectangle is length times of width.

Given,

A rectangle has one side of 10cm

We need to find how fast is the area of the rectangle changing at the instant when the other side is 12 cm  and increasing at 3cm per minute

This can be written as A=10x

Now differentiate with respect to t.

dA/dt=10 dx/dt

increasing at 3cm per minute

dx/dt=3

dA/dt=10 (3)

dA/dt=30

Hence 30 is the area of the rectangle changing at the instant when the other side is 12 cm and increasing at 3cm per minute

To learn more on Rectangle click:

https://brainly.com/question/20693059

#SPJ5

Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x 2 Find H(x+a) - H(x)/a

Answers

Answer:

Step-by-step explanation:

The stumbling block for most people is what exactly do you do the what's in the brackets of something like g(x+ 4) = 2x

The answer is, whatever you see on the left side where g(x) gets modified, you put on the right side wherever you see an x.

In this question

H( x) = x ^2

So if you see anything besides x on the left, then that's what goes on the right for x.

H(x + a) - H(x)/a = (x + a)^2 - (x^2)/a

You can expand this, but I don't see a reason for doing it.

H(x + a) - H(x)/a = (x + a)^2 - (x ^2)/a = x^2 + 2a + a^2 - x^2/a which gets you nowhere.

The volume of one serving of fruit punch
is 3.5 fluid Ounces. How many servings
are there in 29.75 fluid Ounces of
fruit punch?
A. 8.25 Servings
B. 8.5 Servings
C. 9.25 Servings
D. 9.5 Servings

Answers

It's 8.5

If you really want the work w the answer it's because
3.5 29.75
----- =
1 x
cross multiply
3.5x=29.75
divide by 3.5
x = 8.5

How many prime numbers are there between 50
and 75?

Answers

Answer:

All the prime numbers between 50 and 75 are 53, 59, 61, 67, 71 and 73.

Step-by-step explanation:

Answer:

51 53 57 59 61 69 71 73 these are the prime numbers

Which equations represent exponential growth? Which equations represent are exponential decay?
pls help​

Answers

Answer:

When the base is less than 1 it's Decay

When the base is greater than 1 it's Growth

whats 2 + 2 ??!?!?!?!?!?!?!?​

Answers

Answer:

4 duhh... Ur kidding me??

Answer:

22 because 2+2

Step-by-step explanation:

if we put 2 near 2 it will be 22 so the answer is 22

GIVING BRAINLIST!! PLS ANSWER

Trina is buying 12 shirts for the drama club.She will choose a style for the blank shirts and then pay additional charge of $2.75 for each shirt to have the club logo. If Trina cannot spend more than $99, how much can she spend on each blank shirt? Write and solve an inequality to find the possible cost of each blank shirt.

Answers

Answer:

The most she can spend on each blank shirt is $5.50.

Step-by-step explanation:

In order to set up the inequality, we need to write an expression for the total cost of each shirt wherein the price of each blank shirt is "x". Tina needs to buy 12 shirts and there is an additional charge of $2.75 for each logo. The total cost needs to be less than or equal to $99.

This gives us 12 * (x + 2.75) ≤ 99

We can then distribute:

12x + 12 * 2.75 ≤ 99

12x + 33 ≤ 99

Then subtract 33 from both sides:

12x ≤ 66

And finally divide by 12 on both sides:

x ≤ 5.5

Answer:

Step-by-step explanation:

12x + 2.75*12 < 99             Combine 12 * 2.75

12x + 33 < 99                     Subtract 33 from both sides

12x < 99 - 33                      Combine

12x <66                               Dive by 12

x < 66/12

x < 5.50

The very most she can spend is 5.50 on each shirt. Actually it should be 5.49 which will be less than 99. It will come to 65.88 which is just 12 cents less than 99, but it answers the problem. The problem does not use less than or equal which would mean that 99 is the answer ≤

Which is the reciprocal of 1 6/7

Answers

Answer:

7/13

Step-by-step explanation:

You would first have to turn the fraction into an improper fraction to find the reciprocal of the fraction!

1 6/7 = 13/7

Reciprocal means reverse, so reverse the improper fraction of 13/7 to get 7/13!

I hope this helps you!

Solve for M:

3 + 2M = 10 - 6 + 2M

PLS HELP

Answers

Answer:

No solutions

Step-by-step explanation:

We can go through this one step at a time to figure out what M is equivalent to. First, let's write out our whole equation:

3 + 2M = 10 - 6 + 2M

I always like to combine like terms first. It looks like there are two like terms on the right side of our equation... 10 and -6. I can combine those to get 4. Now I have the following equation:

3 + 2M = 4 + 2M

Now, let's remove 2M from both sides.

3 + 2M - 2M = 4 + 2M - 2M

3 ≠ 4

We got an answer of 3 = 4, which is not true (that's why I put a ≠ between them instead of a =). What do we do with this information? Well, since we got an untrue statement as an answer, we know that no number is equivalent to M, or, there are no solutions.

Hopefully that's helpful! :)

Answer:

There are no values of  M  that make the equation true.

Step-by-step explanation:

Today, Ravi burned 1005.7 calories while exercising. Yesterday, he burned 138 calories. How many more calories did Ravi burn today than yesterday?

Answers

Answer:

Ravi burned 867.7 more calories today than he did yesterday.

Step-by-step explanation:

To find how many more calories Ravi burned today than he did yesterday, subtract the number of calories he burned yesterday (138) from the number of calories he burned today (1005.7). This will give us the number 867.7, which is the solution to the problem.

To check this math, we can add 867.7 to 138, which will give us 1005.7, the number of calories Ravi burned today.

Which transformation maps the strip pattern onto itself?

pdpdpdpdpd

A. half-turn
B. vertical reflection
C. glide reflection
D. vertical translation

Answers

The mapping of the strip pattern onto itself is a Glide reflection.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Glide reflection is a combination of reflection over a line and then translation along that line.

As we can see, the mapping of the strip pattern onto itself is a Glide reflection.

Find out more at: https://brainly.com/question/25442628

Answer:

A: Half-turn

Step-by-step explanation:

i took the test and got it wrong due to the wrong answer above.

Graph: f(x) = 4 to the power of 4

Answers

Answer:

how am I supposed to graph?

Step-by-step explanation:

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