solve the equation 13Z/Z+1 =11-3i, Z£C where Z=X+yi X&Y£R?​

Answers

Answer 1

Presumably you mean the equation

[tex]\dfrac{13z}{z+1} = 11-3i[/tex]

Observe that for [tex]z\neq-1[/tex],

[tex]\dfrac{13z}{z+1} = \dfrac{13(z+1) - 13}{z+1} = 13 - \dfrac{13}{z+1}[/tex]

so we can simplify the equation to

[tex]13 - \dfrac{13}{z+1} = 11 - 3i \implies \dfrac{13}{z+1} = 13 - (11 - 3i) = 2+3i[/tex]

Multiply both sides by [tex]\frac{z+1}{2+3i}[/tex].

[tex]\dfrac{13}{z+1}=2+3i \implies \dfrac{13}{2+3i} = z+1 \implies z = \dfrac{13}{2+3i} - 1[/tex]

Rationalize the denominator by introducing its complex conjugate.

[tex]z = \dfrac{13(2-3i)}{(2+3i)(2-3i)} - 1 = \dfrac{26-39i}{2^2+3^2} - 1 = \boxed{1 - 3i}[/tex]


Related Questions

Someone plz help been stuck on this question for the last 2 hours



Paul has $30,000 to invest. His intent is to earn 11% interest on his investment. He can invest part of his money at 7% interest and part at 13% interest. How much does Paul need to invest in each option to make a total 11% return on his $30,000?
7% interest =$?

13% interest =$?

Answers

Answer:

7% interest = $10000

13% interest = $20000

Step-by-step explanation:

Let the amount invested at 7% interest be x.

Let the amount invested at 13% interest be y.

Thus;

x + y = 30000 - - - (eq 1)

We want to find out how much Paul needs to invest in each option to make a total 11% return on his $30,000.

Thus;

0.07x + 0.13y = 0.11(30000)

Multiply through by 100 to get rid of the decimal;

7x + 13y = 0.11(30000 × 100).

7x + 13y = 330000 - - - (eq 2)

From eq 1, x = 30000 - y

Put this for x in eq 2 to get;

7(30000 - y) + 13y = 330000

210000 - 7y + 13y = 330000

6y = 330000 - 210000

6y = 120000

y = 120000/6

y = $20000

x = 30000 - 20000

x = $10000

Thus;

Amount invested at;

7% interest = $10000

13% interest = $20000

A man earns $1500 a week. He saves $500. What percentage did he spend?

Answers

Answer:

3313%

Step-by-step explanation:

He spent 66.67%. Check below for reference:


1. What is the range of frequencies a human ear can hear?

Answers

Answer:

Humans can detect sounds in a frequency range from about 20 Hz to 20 kHz.

(Human infants can actually hear frequencies slightly higher than 20 kHz, but lose some high-frequency sensitivity as they mature; the upper limit in average adults is often closer to 15–17 kHz.)

Please help marking brainliest for correct answer

Answers

The answer is alternative exterior.

Answer:

alternate exterior

Step-by-step explanation:

Math will give brainliest

Answers

Answer: 312

Step-by-step explanation: i just times it

Answer:

Mutiply 24 and 13

24×13=312

312cm3

simplify the expression 4x+2-1/2x

Answers

Answer:

7/2 x  + 2

Step-by-step explanation:

4x+2−

1

2

x

A boy runs a distance of 200km in 25seconds. What is his average speed

Answers

Answer:

8 km average speed

Step-by-step explanation:

Answer:

His average speed is 28,800 km per hour.

Step-by-step explanation:

He runs 480 km per minute. Then I multiply 480 by 60 to get 28,800 km.

:))

please help me out. is it A B C D?​

Answers

The answer is: B sorry if I’m wrong

(2a+5)³ is equal to 8a³+60a²+________?​

Answers

the answer is will be +50a+125

One way an author can call attention to the order of events in a narrative is by using

setting

description

dialogue

transitions

Answers

is by using transitions cuz it allows the reader to understand when there’s a shift in events but also the oder

22. Write the inequality for the graph shown below.


Help. Please.

Answers

The inequality is y greater or equal to -3/2x + 1

Steps are on paper
If you need more explanation about this, comment

Find the distance between the two points (-5, -2) and T(-3, 4).

Answers

Answer:

[tex]\displaystyle d = 2\sqrt{10}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinates (x, y)

Algebra II

Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Step-by-step explanation:

Step 1: Define

Point (-5, -2) → x₁ = -5, y₁ = -2

Point (-3, 4) → x₂ = -3, y₂ = 4

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Substitute in points [Distance Formula]:                                                       [tex]\displaystyle d = \sqrt{(-3+5)^2+(4+2)^2}[/tex][√Radical] (Parenthesis) Add:                                                                        [tex]\displaystyle d = \sqrt{(2)^2+(6)^2}[/tex][√Radical] Evaluate exponents:                                                                    [tex]\displaystyle d = \sqrt{4+36}[/tex][√Radical] Add:                                                                                               [tex]\displaystyle d = \sqrt{40}[/tex][√Radical] Simplify:                                                                                         [tex]\displaystyle d = 2\sqrt{10}[/tex]

brainlist-brainlist-brainlist

Answers

Answer:

triangle

Step-by-step explanation:

The cross section is a triangle.

Answer:

i think either a square or rectangle

Step-by-step explanation:

140 es múltiplo de 100​

Answers

Answer:

Step-by-step explanation:

No it isn't. 140/100 is NOT a whole number so 140 isn't a multiple of 100.


Someone plz helpppp

A chemistry teacher needs to mix a 40% salt solution with a 70% salt solution to make 25 qt of a 52% salt solution. How many quarts of each solution should the teacher mix to get the
desired result?
40% salt solution=?qt
70% salt solution=?qt

Answers

Answer:

Step-by-step explanation:

We assume we need x qt of 40% and y qt of 70%

40/100 x + 70/100 y = 52/100 (x+y)

So 3y = 2x, which means y = 2/3x

And we know that x + y = 25qt

So x + 2/3x = 25qt

So x = 15 and y = 10

Q-U-E-S-T-I-O-N: Whats 1000000000000000000000000 multiplyed by 20000000
Its a weird word :/

Answers

Answer:

2e+31

Step-by-step explanation:

WORTH 10 POINTS :)



Bo paid with 1/2 of his paycheck about 1/5 of the remainder in savings. The rest of his paycheck he divided equally among the college accounts of his 3 children.

1. What fraction of his paycheck went into each child's account?

2. If bo deposited $400 in each child's account, how much money was in Bo's original paycheck?​

Answers

Answer:for college, 1-1/2-1/5 = 3/10. Divided by 3 children, 3/10 /3 = 1/10

B. 400 = 1/10 of the total (from above), so 400 = x/10. x = 400*10 = 4000

Step-by-step explanation:

Answer:

1. 1/6 2. $2400

Step-by-step explanation:

If Bo had 1/2 of his paycheck leftover to divide among his 3 kids, 1/2 divided by 3 is 1/6.

If 1/6 of his paycheck is $400, then all 6/6 of his paycheck would be $2400.

How to do 5x+2=52? ME GIVE BRAIN DO IT NOWWWWW

Answers

Hi there!

52 subtract by 2 is 50 and then dividing by 5 would be 10.

So x would be 10.

A family borrows money for a rainforest tour. The simple annual interest rate is 12%. The loan is paid after 3 months. What is the total amount paid for the tour?

Answers

Answer:

1,266.90

Step-by-step explanation:

1. 940 + 170 + 120 = 1,230

2. 1,230 x 0.12 x 0.25 = 36.9

3. 36.9 + 1,230 = 1,266.90 (FINAL ANSWER)

There are 5 more than twice as many students taking Algebra 1 than taking Algebra 2. If there are 44 students taking Algebra 2,
what is the least number of students who could be taking Algebra 1? The least number of students is (pe numbers only)

Help asap

Answers

Answer: 54

Step-by-step explanation:

I NEED HELP PLSSSSSSS​

Answers

Variable, constant, hole

helppppppppppppppppppppp

Answers

We can apply the Pythagorean theorem:

c= (SQ)

a=RQ = 4

b=RS = 4

c²=a²+b²

c=√(16+16)

c=√32

c=4√2

SV=0,5*SQ

SV=0,5*c

SV=√2

Mikey buys an assorted box of chocolates that contains 18.61 ounces of dark chocolate and 37.23 ounces of milk chocolate. how much do the chocolate weigh in total?

Answers

Answer:

55.84 oz

Step-by-step explanation:

Hope this will help

if_ is added to a number, the sum will remain the same. Hence _ is called the _in the whole number​

Answers

Answer:

Step-by-step explanation:

If 0 is added to a number, the sum will remain the same.

At 1:00 a.m., the temperature is 58º. At 9:00 a.m., the temperature is 76º. Find the rate of change in degrees per hour during this time.​

Answers

Answer:

1 AM = 58 Degrees

9 AM = 76 Degrees

Difference of temperate between the times:

18 Degrees

Divide every hour that passes by the total difference of temperate, which the hours are: 2, 3, 4, 5, 6, 7, 8, 9

18 / 8 = 2.25

Which means, the rate of change in degrees per hour is 2.25 degrees.

Step-by-step explanation:

Can somebody please answer the question giving brainliest!

Answers

Answer:

A counter clockwise

Step-by-step explanation:

Will mark Brainlyist help me fill out the chart

Answers

Answer:

The working is done in the image attached.

How many 3/5 are in 7

Answers

Answer:

11.6

Step-by-step explanation:

7 ÷ ⅗ = 11.6

I hope this answer is satisfactory. Please comment if you have any concerns.

Answer:

35/3 or 11 2/3

Step-by-step explanation:

This is a division problem.

We need to divide 7 by 3/5.

7 / 3/5 = 7/1 / 3/5 = 7/1 * 5/3 = 35/3 = 11 2/3

Answer: 35/3 or 11 2/3

An advertising agency notices that approximately 1 in 50 potential buyers of a product sees a given magazine ad, and 1 in 8 sees a corresponding ad on television. One in 100 sees both. One in 4 actually purchases the product after seeing the ad, 1 in 10 without seeing it. What is the probability that a randomly selected potential customer will purchase the product

Answers

Answer:

Probability = 0.12025

Step-by-step explanation:

P (Am) = 1/50 = 0.02       {Magazine ad}

P (At) = 1/8 = 0.125         {Television ad}

P (Am ∩ At ) = 1/100 = 0.01      {Both ads}

P (Am U At) = P (Am) + P (At) - P (Am ∩ At )

= 0.02 + 0.125 - 0.01

P (Am U At)  = 0.135       {Person sees either ad}

P (Am' ∩ At') = 1 - P (Am U At)

P (Am' ∩ At')  = 1 - 0.135 = 0.865      {Person sees none ad}

Prob (Purchase) = Prob (Purchase with ad) + Prob (purchase without ad)

P (P/ A) = 1/4 = 0.25 , P (P / A') = 1/10 = 0.1

P (P) = (0.25) (0.135) + (0.1) (0.865)

= 0.03375 + 0.0865

0.12025

what is the area of this parralelogram? h=4 inch b=7 inch

Answers

Answer:

28cm^2

Step-by-step explanation:

4 x 7

Answer:

no sé nada de inglés we ya me entiendes si supiera te ayudará pero eso está difícil busca por internet

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