How do I determine z ∈ C:

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

Answers

Answer 1

Simplify the coefficient of z on the left side. We do this by rationalizing the denominators and multiplying them by their complex conjugates:

[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3-2i}{1+i}\cdot\dfrac{1-i}{1-i} - \dfrac{5+3i}{1+2i}\cdot\dfrac{1-2i}{1-2i}[/tex]

[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{(3-2i)(1-i)}{1-i^2} - \dfrac{(5+3i)(1-2i)}{1-(2i)^2}[/tex]

[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3 - 2i - 3i + 2i^2}{1-(-1)} - \dfrac{5 + 3i - 10i - 6i^2}{1-4(-1)}[/tex]

[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3 - 5i + 2(-1)}2 - \dfrac{5 - 7i - 6(-1)}5[/tex]

[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{1 - 5i}2 - \dfrac{11 - 7i}5[/tex]

[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{1 - 5i}2\cdot\dfrac55 - \dfrac{11 - 7i}5\cdot\dfrac22[/tex]

[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{5 - 25i - 22 + 14i}{10}[/tex]

[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = -\dfrac{17 + 11i}{10}[/tex]

So, the equation is simplified to

[tex]-\dfrac{17+11i}{10} z = \dfrac12 - \dfrac{2i}5[/tex]

Let's combine the fractions on the right side:

[tex]\dfrac12 - \dfrac{2i}5 = \dfrac12\cdot\dfrac55 - \dfrac{2i}5\cdot\dfrac22[/tex]

[tex]\dfrac12 - \dfrac{2i}5 = \dfrac{5-4i}{10}[/tex]

Then

[tex]-\dfrac{17+11i}{10} z = \dfrac{5-4i}{10}[/tex]

reduces to

[tex]-(17+11i) z = 5-4i[/tex]

Multiply both sides by -1/(17 + 11i) :

[tex]\dfrac{-(17+11i)}{-(17+11i)} z = \dfrac{5-4i}{-(17+11i)}[/tex]

[tex]z = -\dfrac{5-4i}{17+11i}[/tex]

Finally, simplify the right side:

[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{5-4i}{17+11i} \cdot \dfrac{17-11i}{17-11i}[/tex]

[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{(5-4i)(17-11i)}{17^2-(11i)^2}[/tex]

[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{85 - 68i - 55i + 44i^2}{289-121(-1)}[/tex]

[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{85 - 68i - 55i + 44(-1)}{410}[/tex]

[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{41 - 123i}{410}[/tex]

[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{41 - 41\cdot3i}{410}[/tex]

[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{1 - 3i}{10}[/tex]

So, the solution to the equation is

[tex]z = -\dfrac{1-3i}{10} = \boxed{-\dfrac1{10} + \dfrac3{10}i}[/tex]


Related Questions

What is the value of g(1)? What is the value of g(-12)? For which of the following x-values is g(x)=-6

Answers

The numeric values of the function are given as follows:

g(1) = 4.g(-12) = -10.g(x) = -6 for -8 ≤ x < -1.

g(1)

When x = 1, the function has a closed value on the graph at y = 4, hence:

g(1) = 4.

g(-12)

When x = -1,2 the function is passing through y = -10, hence the numeric value is given as follows:

g(-12) = -10.

g(x) = -6

The function is passing through the horizontal line y = -6 when -8 ≤ x < -1, hence:

g(x) = -6 for -8 ≤ x < -1.

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what is the estimate of 45.15

Answers

Answer:

The estimate would be:

(one of them :)

45 (if your doing the entire number)

0 (if your rounding out of 100)

45.2 (nearest hundredth)

45.0 (nearest tenth)

50 (nearest tens)

Hopefully one of these works for you.

The cost of a ride in a taxi is $2.50 for the first half-mile plus a constant amount per half-mile after that. The sequence below shows the pattern of numbers that appear on the driver's screen.


2.50, 2.75, 3.00. 3.25, 3.50, 3.75


Part A: Write a recursive function that can be used to determine f(x), the cost in dollars, for a ride in the taxi of, x, half-miles.

Answers

Answer:  2.50 + 0.35(15.75-1)*4 = $23.15 is the answer

Step-by-step explanation: Hope this helps!

There are 564 men and women working in a factory.
There are twice as many women as men.
How many men are working in the factory?

Answers

Answer:

564x2=1128 men

Step-by-step explanation:

Answer:

there are1139 women are working in the factory

AYUDA!!!!!!! Pls help me answer

Answers

You don't mention what's the question

E is 54, f 126. D 126

f(x)= -2x^3 +14x -8
g(x)= 2x+6

Answers

Answer:

F(2x+6)=-16x^3-144x^3-404x-356

Step-by-step explanation:

Solve the right triangle. a = 2.2 m, B = 37.7°, C = 90° 4) A) A = 52.3°, b = 0.6 m, c = 2.3 m B) A = 52.3°, b = 1.7 m, c = 2.8 m C) A = 52.3°, b = 3.2 m, c = 3.9 m D) A = 52.3°, b = 3.2 m, c = 2.8 m

Answers

Answer:

B) A = 52.3°, b = 1.7 m, c = 2.8 m

Step-by-step explanation:

We know that it is a right angle triangle because C = 90°

because of that we can do 180 - 90 + 37.7

which is a=52.3

Because it is a right angle triangle, we can use sin, cos,tan

I will use sin to find the side of c

2.2 is a

sin 52.3 = 2.2/x

x= 2.2/ sin 52.3

x=2.78

You could do cos or tan but the pythagorean theorem for me is much faster

so it looks like this, a^2+b^2 =c^2

in this case we have both a and c we want b

so we rearrange

c^2-a^2=b^2

2.78^2-2.2^2= b^2

[tex]\sqrt{2.89}[/tex]=b

1.7=b

therefore it would be this option B) A = 52.3°, b = 1.7 m, c = 2.8 m

what is the intercepts of the line?

x-intercept and y-intercept

4x-1=3y+5

Answers

Answer:    X (3/2,0)   Y (0,-2)

Step-by-step explanation:

maya picks 16 vegetables 6 of them are carrots the rest are cucumbers then she gives away 5 cucumbers how many cucumbers does maya have now

Answers

Answer:

5

Step-by-step explanation:

First subtract 6 from 16 to find how many cucumbers she has,

16 - 6 = 10

Now we know she has 10 cucumbers.

Subtract 5 from the 10 cucumbers to find out how many she has after giving away 5.

10 - 5 = 5

After subtracting the 5 cucumbers she gave away, we are left with 5

This means Maya has 5 cucumbers now

What is 34÷18? Explain or show your reasoning.

Answers

Answer:

1.8889

Step-by-step explanation:

Leah's bill for breakfast at a restaurant was $68. She left an 18% tip. What was the amount of the tip?​

Answers

Answer:

55.76

Step-by-step explanation:

55.76

18% of $68 would be $12.24

no link fast but righ and if you get the answer right can you help me with other question

Answers

Answer:

12 inches

Step-by-step explanation:

The volume of a cone is given by

V = 1/3 pi r^2 h  where r is the radius and h is the height

113.04 = 1/3*3.14 ( 3)^2 h

113.04 = 9.42 h

Divide each side by 9.42

113.04/9.42 = h

12 = h

12 inches

Answer:

Height = 12 in

Step-by-step explanation:

Volume Cone = 1/3(πr²h)

113.04 = 1/3(3.14)(3²)(h)         [tex]\longmapsto[/tex]           Note that the 1/3 and 9 simplify

113.04 = 3.14(h)(3)

37.68 = 3.14(h)

h = 12

-Chetan K

Mr. Wilhelm got a $2 discount on
the purchase of 5 bags of peat moss.
If he paid $7.40, what was the price
for a bag of peat moss before the
discount?

Answers

Answer:

9.40

Step-by-step explanation:

7.40+2.00=9.40

A gopher lives in an underground burrow. It starts at a certain point, p, underground and digs straight down to triple its distance under
the surface. It then climbs straight down another 2 feet. Its final position is deeper than 8 feet under the surface.
What was the gopher's original position, p, relative to the surface?
Enter your answer in the box to complete the inequality.
р

Answers

Answer:

The answer is <-2

Step-by-step explanation:

Answer: I'm late but here you go

Step-by-step explanation:

Is x = 1 a function?

Answers

Yes x = 1 is a function.
Hope this helps :(

Answer:

Yes

Step-by-step explanation:

It is a constant linear function, which is in fact a function.

Have a nice day!

   I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Juan wants to buy a video game for $63. He saves $12 every Friday. Part A. Create an equation to represent Juan's total savings, y, in dollars, after x Fridays. y​

Answers

Answer:

Answer in explanation.

Step-by-step explanation:

An equation to represent Juan's total savings y, in dollars, after x Fridays will be;

⇒ y = 12x

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Juan wants to buy a video game for $63.

And, He saves $12 every Friday.

Now,

Let total dollars after x Friday = y

And, He saves $12 every Friday.

So, We can formulate;

⇒ Total money (y) = 12x

⇒ y = 12x

Thus, An equation to represent Juan's total savings y, in dollars, after x Fridays will be;

⇒ y = 12x

Learn more about the mathematical expression visit:

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Is 6,702,512 divisible by 9?

Answers

Yes it is also add more points next time

$250, 3.4%, 3 years what would my interest be?

Answers

Ur interest should be 3.4 divided by 250 times 3

The graph of f(x) = x2 has been shifted into the form f(x) = (x - h)2 + k:
5
365
What is the value of k? (1 point)
0 1
0-1
O-2
O 2

Answers

The value of k would be 1. This is because the points (h, k) is the vertex and since k is the y-value of the vertex, we can see from the graph that it’s 1.

Pease someone help me with this.

I just need two more tiles to create but I don't know how they would look like.

I will show below what I have filled and what the question is asking.

Question: How many different layouts are possible for a path that is five feet long? Draw them all here:

Answers

Answer:

go get that girl

Step-by-step explanation:

sike  you use what you got the first time

Answer:

If the path is 5 feet long, then you could only have a limited amount of layouts...so- you could only have 5 limited spaces in one layout, making it 5 DIFFERENT LAYOUTS.

(I don't know what they're really asking, but I did what makes sense, SORRY if I'm wrong, I'm going to try and solve it better/draw it.)

This circle is centered at the point (3,2) and the length of its radius is 5 what is the equation of the circle

Answers

Answer:(x-3)² + (y-2)² = 25

Step-by-step explanation:

A circle's equation is (x-h)² + (y-k)² = r². When centered at the origin, h and k equal 0. If you shift the circle, say, one unit up, then k equals 1, and the equation is x² + (y-1)² = r².

So for your circle, the equation would be (x-3)² + (y-2)² = 5² or (x-3)² + (y-2)² = 25.

Answer:

(x - 3)² + (y - 2)² = 25

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

Here (h, k ) = (3, 2 ) and r = 5 , then

(x - 3)² + (y - 2)² = 5² , that is

(x - 3)² + (y - 2)² = 25 ← equation of circle

A bag contains 11 apples and 6 oranges. If you select 6 pieces of fruit without looking, how many ways can you select exactly 5 apples

Answers

Answer:

you have a 11/17 percent chance of getting an apple

Step-by-step explanation:

if there are 11 apples and 6 oranges. 11 out of 17 times you will get an apple

The price of an item has been reduced by 85%. The original price was $37.

Answers

Answer:  Multiply the original price by the decimal form of the percent and subtract that from the original price.

37*0.85=31.45

37-31.45=5.55

Answer: New price is $5.55

Abigail earned $10.26 for babysitting her cousin for 3 hours. How much did she earn in each hour?

Answers

Divide total earned by number of hours:

10.26/3 = $3.42

She earned $3.42 per hour

Each hour she earns $3.42

The diagram below shows two parallel lines, m and n, cut by a transversal, k. Angles A, B, and C are shown in the diagram

A student writes a proof to show that the corresponding angles, A and B, are congruent. The student's proof is shown below

A. Both reason 2 and Reason 3 are correct as shown in the table
B. Reason 2 is correct, but Reason 3 should "Alternate interior angles are congruent"
C. Reason 2 should be "Alternate interior angles are congruent," but Reason 3 is correct
D. Both Reason 2 and Reason 3 should be "Alternate interior angles are congruent"

(look at picture to understand better)

Answers

9514 1404 393

Answer:

  B

Step-by-step explanation:

Angles A and C are vertical angles; angles B and C are alternate interior angles. Only line 3 of the proof is in error.

The applicable description is found in choice B.

what would be the volume of the cone that has the same measurement as the cylinder above in the pic

do the working also ​

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

Volume of cone will be ~

[tex]\fbox \colorbox{black}{ \colorbox{white}{volume} \:  \:  \:   \:  \: \colorbox{white}{=}  \:  \:  \:   + \colorbox{white}{462 \: cm³ }}[/tex]

[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]

Let's find the volume of cone with ~

radius (r) = 7 cm

height (h) = 9 cm

And as we know, volume of cone is equal to ~

[tex] \dfrac{1}{3}\pi {r}^{2} h[/tex]

now, let's plug in the values and find the volume ~

[tex] \dfrac{1}{ \cancel{3} }\times \dfrac{22}{\cancel{7}} \times \cancel{7 }\times 7 \times \cancel{9}[/tex]

[tex]1 \times 22 \times 7 \times 3[/tex]

[tex]462 \: \: {cm}^{3} [/tex]

Volume of cone is 462 cm³ = 462 ml

geomtry plzzz help 15 points

Answers

Answer:

19

Step-by-step explanation:

they give you xz, and they want half, so just divide 38 by 2

Apply the distribute property, substitute the given numerical value given:
9(-3r -11), r=10

Answers

Answer:

-369

Step-by-step explanation:

Replace r with 10.

9(-3(10)-10))

9(-30-11)

9*-30+9*-11

-270+ -99

-369

Hope this helped. :)

Please solve for a: b = 2 - (1/a)

Answers

[tex]b = 2 - \dfrac 1a\\\\\implies ab = 2a -1\\\\\implies 2a -ab = 1\\\\\implies a(2-b) =1\\\\\implies a = \dfrac 1{2-b}[/tex]

-3y<-14 i dont get the dam question

Answers

Answer:

Step-by-step explanation:

-3y<-14

divide both sides by -3

y<4.67

i’m not exactly sure what the question is asking or what you’re trying to find, but this is what i could figure out.

Answer:

y>14/3

I'll provide the step by step solution too.

=3y÷(-3)>-14÷(-3)

y>-14÷(-3)

y>14÷3

turn it into a fraction

y>14/3

hence your given answer above

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