1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Bogdan [553]
2 years ago
5

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

Mathematics
1 answer:
labwork [276]2 years ago
5 0

Presumably you mean the equation

\dfrac{13z}{z+1} = 11-3i

Observe that for z\neq-1,

\dfrac{13z}{z+1} = \dfrac{13(z+1) - 13}{z+1} = 13 - \dfrac{13}{z+1}

so we can simplify the equation to

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

Multiply both sides by \frac{z+1}{2+3i}.

\dfrac{13}{z+1}=2+3i \implies \dfrac{13}{2+3i} = z+1 \implies z = \dfrac{13}{2+3i} - 1

Rationalize the denominator by introducing its complex conjugate.

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

You might be interested in
Solve 3x − 2 = 37. please help me
lyudmila [28]

Answer:

x=13

Step-by-step explanation:

1. Isolate the variable

3x - 2 = 37

     +2 = +2

2. Divide the equation by the coefficient

3x = 39

/3    /3

3. Answer

x = 13

8 0
3 years ago
Read 2 more answers
Help with the attachment please it would be so much help!!!!
Anna35 [415]

Answer:

angle BED and angle DEB are the answers.

3 0
3 years ago
A tree is 117 inches tall. How tall is it in feet and inches?<br> ?
xz_007 [3.2K]

Answer:

9 ft and 9 inches

Step-by-step explanation:

there are 12 inches in a foot

1ft = 12in

2ft = 24 in

3ft = 36 in

4ft = 48

and so on

9 ft = 108 inches which is the closes to 117.

So we have 9 ft

subtract 117 from 108, which is 9 inches left over

6 0
3 years ago
Solve for x and y-intercepts and show the work! Im on a timed test!<br><br>2x - 3y = 12
REY [17]

Answer:

Equation: y=2/3x-4

y intercept is (0,-4)

x intercept is (6, 0)

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Help me with this 1,2,3. For each sequence, Determine with whether it appears to be arithmetic If it does find a common differen
pshichka [43]

Problem 1

<h3>Answer: Arithmetic, common difference = -4</h3>

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

Explanation:

Pick any term of the sequence, and subtract off the previous term to find that,

  • term2 - term1 = -12 - (-8) = -12 + 8 = -4
  • term3 - term2 = -16 - (-12) = -16 + 12 = -4
  • term4 - term3 = -20 - (-16) = -20 + 16 = -4

Each time we get the same result, so that means we have an arithmetic sequence with common difference -4

This indicates that adding -4 to each term, or subtracting 4 from each term, will generate the next one.

Eg: term2 = term1 - 4 = -8-4 = -12.

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

Problem 2

<h3>Answer: Arithmetic, common difference = 5</h3>

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

Explanation:

Similar to problem 1, this sequence is also arithmetic because we add on 5 to each term to get the next one

  • -6+5 = -1
  • -1+5 = 4
  • 4+5 = 9

Or you could subtract adjacent terms as done in problem 1, to find that the common difference is 5.

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

Problem 3

<h3>Answer: Not arithmetic</h3>

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

Explanation:

Unlike the previous two problems, this sequence is not arithmetic.

We can see that

  • term2 - term1 = 12 - 3 = 9
  • term3 - term2 = 48 - 12 = 36

The gaps of 9 and 36 aren't the same. We need the same common difference between any adjacent terms to have an arithmetic sequence.

This sequence is instead geometric because

  • term2/term1 = 12/3 = 4
  • term3/term2 = 48/12 = 4
  • term4/term3 = 192/48 = 4

Each quotient is 4, showing the common ratio is 4. To find the next term, we multiply the current term by 4. So the next term after 192 would be 4*192 = 768, then 4*768 = 3072 is next, and so on.

3 0
3 years ago
Other questions:
  • How is the quadritael ABCD not a rhombus nor rectangle? I already prove it is a parallelogram​
    6·1 answer
  • Evaluate -17 - (-4 2/3).Express your mixed number in simplest form
    12·1 answer
  • What is 95% of 800? 680 720 760 795​
    5·1 answer
  • What is the value of 5(7× +5), when X=10 ?
    12·2 answers
  • A school club is raising money for a trip, and needs to reach $10,000. Their fundraising progress is modeled by the function
    12·2 answers
  • Q2.<br>a) Is the equality √a^4 = a valid for all values of a? Explain.<br>​
    10·1 answer
  • 1,2,3 or 4?<br><br> Look at the picture. <br> Thank u!
    7·1 answer
  • Mr. Duncan creates a pop quiz for his students. On the quiz, students must order the following numbers from least to greatest.
    15·1 answer
  • Find f(3.5) if f(x) = (4x - 2)/10
    5·1 answer
  • Scored 28 points in his basketball game by shooting only two point and three point shots. He scored a total of 13 baskets
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!