zz* + 3iz = p + 9i
where z is a complex number and p is a real constant.
Given that this equation has exactly one root, determine the complex number z

Answers

Answer 1

Step-by-step explanation:

I need to use the fact that it has exactly one root to find the y part - do I use the quadratic formula on the last bit I have written?

I have x already and z = x+iy

Answer 2

3i and 3 are two complex numbers that fulfill this equation.

What are complex numbers?

A complex number is a number of the form (a + bi), where [a] and [b] are real numbers and [i] is equal to [tex]\sqrt{-1}[/tex]. The general form of the complex number representation is (a + ib). In this, [a] is called real part and [ib] is called imaginary part.

We have -

zz* + 3iz = p + 9i

Assume the complex number to be -

z = a + ib

Then -

(a + ib)(a - ib) + 3i(a + ib) = p + 9i

a² + b² + 3ai + 3bi = p + 9i

(a² + b²) + i(3a + 3b) = p + 9i

So -

3(a + b) = 9

a + b = 3

(a² + b²) = p

Now -

Assume p = 9

Then -

a + b = 3

a² + b² = 9

we get two possible values -

(a, b) = (0, 3)

and

(a, b) = (3, 0)

It can be seen that the values of complex number depend upon the value of p. For p = 9, two complex numbers fulfill this equation -

0 + i3 = 3i

3 + i0 = 3

Therefore, 3i and 3 are two complex numbers that fulfill this equation.

To solve more questions on complex numbers, visit the link below-

brainly.com/question/617146

#SPJ2


Related Questions

The angle of elevation from Nathan to a lighthouse is 74°.
If the lighthouse is 112 feet tall, how far is Nathan from the
base of the lighthouse?

Answers

Answer:

Nathan is 36.3910059 ft from the base of the lighthouse.

Step-by-step explanation:

So to find the base, you have to find the tan (both legs) of the right triangle that the lighthouse makes. The angle of Nathan to the lighthouse is 74° so to find the distances, you have to do the tan(72) = opp/adj

The opposite is 112, and we have to find the adjacent.

tan(72) = 112/adj

3.07768354 = 112/adj

adj = 112/3.07768354

adj = 36.3910059

Please help asap i’ll give brainly it's due in 30 min

Answers

Answer:

[tex]2\sqrt{3[/tex]

Step-by-step explanation:

HELP WILL GIVE BRANLIEST!

No links!!

Answers

Answer:

32 ftEach base floor tile is 5ft and there's 4 tiles so 5x4=20

Next,there are 4 walls each wall is 3ft 3x4=12

Now you add your answers which is 20+12=32

Hope that helps

Are the cylinders similar? Why or why not?​

Answers

Answer: are cylinders similar to what its not asking so id.kkk

Step-by-step explanation:

answer choices:
A. 42 °
B. 47°
C. 48°
D. 41°
can some one help me please

Answers

Answer:

D. 41°

Step-by-step explanation:

[tex](3x + 9) \degree = 132 \degree \\ (vertical \: \angle s) \\ 3x + 9 = 132 \\ 3x = 132 - 9 \\ 3x = 123 \\ x = \frac{123}{3} \\ x = 41 \\ \\ \because m\angle QRS =x\degree \\\therefore m\angle QRS = 41\degree [/tex]

D.41....I think QRS is a right triangle but I can’t see that well. If it’s a right triangle that leaves a 30,60,90 approach.

A report on the nightly news broadcast stated that 10 out of 108 households with pet dogs were burglarized and 20 out of 208 without pet dogs were burglarized. Suppose that this data is used to test the claim that the proportion of households with dogs that are burglarized is the same as the proportion of households without dogs that are burglarized. What would be the test statistic for this test

Answers

Answer:

The answer is "0.9184".

Step-by-step explanation:

This problem is assisted by data analysis:

Its overview hypothesis test to two sample proportions:

[tex]p_1 :[/tex]percentage of population contributions 1

[tex]p_2:[/tex]percentage of population contributions 2

[tex]\to p_1 - p_2:[/tex] proportion difference

[tex]\to H_0 : p_1 - p_2 = 0\\\\\to H_A : p_1 - p_2 ? 0[/tex]

Calculating the Hypothesis test values:

[tex]Diff \ \ Count1 \ \ Total1 \ \ Count2 \ \ Total2 \ \ Sam. Diff. \ \ Std. Err.\ \ Z-Stat \ \ P value\\\\[/tex]

[tex]p_1 - p_2\ \ 10\ \ 108\ \ 20\ \ 208\ \ -0.0035612536\ \ 0.034766147\ \ -0.10243452 \ \ 0.9184[/tex]

So, the [tex]P - value = 0.9184[/tex]

4. What number comes next. Whats my rule?
34,41,. 55,63,
Whats my rule?
(2 Points)
Enter your answer

Answers

48 then 70. Your rule is add 7.

Julio has $1026 worth of $10 and $11 stock shares. The number of $11 shares is six more than twice the
number of $10 shares. How many of each does he have?
The number of $10 shares: |
Enter an integer or decimal number (more..
The number of $11 shares:
Submit Question

Answers

Step-by-step explanation:

just follow the answer good luck

24. ZABC and ZDEF are linear pairs. Which of the following is true?

a. If m ABC = 2m DEF, then m ABC = 120 and m DEF = 60.

b. If m ABC = m DEF + 40, then m ABC = 140 and m DEF = 40.

c. If m ABC = m DEF - 30, then m ABC = 30 and m DEF = 150.

d. If m ABC = 3m DEF, then m ABC = 130 and m DEF = 60.

Answers

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

ASAP Point A, located at (-3, -3) is translated 6 units up, resulting in the location of point A'. What other transformation would result in the same location for point A'? A reflection in the x-axis A translation of 6 units to the left A reflection in the y-axis A rotation of 180°

~I KNOW ITS NOT A REFLECTION IN THE Y-AXIS

Answers

Answer:

(3,3)

Step-by-step explanation:

A reflection of this across the y-axis is (-3,3). A reflection of Point A, (-3,-3), over the x-axis is also (-3,3).

Plss help mart brain list

Answers

The answer is x=14. Just lmk if you need the work too

Answer:

X=14

Step-by-step explanation:

Hope this helps , good luck ^^

PLEASE HELP ME PLEASE

Answers

Answer:

Solution :-

Mean = 75 + 68 + 75 + 92 + 105/5

Mean = 415/5

Mean = 83

None of option is correct

[tex] \\ [/tex]

A triangle has vertices T(-2,4), E(6,2), and D(1,-1). Is ATED a right triangle?
No, this is not a right triangle.
Yes, because ED is perpendicular to DT which makes a right angle.
Yes, because TE is perpendicular to DT which makes a right angle.
Yes, because TE is perpendicular to ED which makes a right angle.

Answers

Answer:

B. Yes, because ED is perpendicular to DT which makes a right angle.

Step-by-step explanation:

Plot the given points and connect in pairs to get a triangle.

Visually we can say it is a right triangle as legs TD and ED seem perpendicular.

Let's confirm this by finding the slopes.

Slope of TD:

m = (-1 - 4)/(1 -(-2)) = -5/3

Slope of ED:

(-1 - 2)/ (1 - 6) = -3/-5 = 3/5

Product of the slopes is:

-5/3*3/5 = -1

This confirms DT⊥ED

Correct choice is B

if you let a soap in the floor does the soap is cleaning the floor or is the soap getting dirty?¿​

Answers

Answer:

que

Step-by-step explanation:

no se

Answer:

soap is getting dirty regardless if there is water on the floor.

Step-by-step explanation:

PLEASE HELP!!!! THERE IS A PICTURE SUBMITTED!

Answers

Answer:

C: 4 hours

Step-by-step explanation:

Mean = Σxn/n

Σx/n = ((2 × 4) + (3 × 5) + (4 × 6) + (5 × 3) + (6 × 3) + (7 × 0) + (8 × 1))/(4 + 5 + 6 + 3 + 3 + 0 + 1)

Σx/n = 88/22

Σx/n = 4 hours

DLMN is a quadrilateral inscribed in a circle. If mÐD = 84° and mÐN = 74°, find mÐL.

Answers

9514 1404 393

Answer:

  angle L = 106°

Step-by-step explanation:

Opposite angles in an inscribed quadrilateral are supplementary.

  ∠L = 180° -∠N

  ∠L = 180° -74° = 106°

Given that £1 = $1.62
b)
a) How much is £650 in $?
b) How much is $405 in £?

Answers

Answer:

A) £650 = $1053

B) $405 = £250

Step-by-step explanation:

For a) Since £1 is equal to $1.62 you would just do £650 times 1.62 to get $1053

For b) Since £1 is equal to $1.62 you would do $405 divided by 1.62 to get £250

What is fifty-two billion in expanded form?

Answers

Hsveheveheehegeheneebevevev

HELP SOMEONE PLZ HELP IM STRUGGLING PLZZ I NEED HELP I WILL MARK BRAINLEST​

Answers

Answer:

Without any background information on the text such as what the physical environment is and what the economic activities are. I can't really help you.

solve the inequality 3(y+5)>21

Answers

Answer:

y > 2

Step-by-step explanation:

1) [tex]3(y+5)>21[/tex]

Divide both sides by 3.

2) [tex]y+5>7[/tex]

Move the constant to the right side and change it's sign.

3) [tex]y>7-5[/tex]

Subtract the numbers.

4) [tex]y>2[/tex]

What is the volume of the cone?
Use 3.14 for π, and round to the nearest tenth.

Answers

Volume =  

1  πr2h

3

=  

1 ×π×22×7

3

=  29.321531433505 miles3

This is relative frequency table. Can someone help?

Answers

59 is the answer to this question

Answer:

Step-by-step explanation:

59 kids are playing video games.. we are maybe missing some of the instructions?  or are there not any more?  

Find the value of 4/81

Answers

Answer:

0.04938271605

Step-by-step explanation:

4/81

=0.04938271605

pls mark as brainliest

Answer:

0.04938271605

Step-by-step explanation:

4/81=0.04938271605

=0.05

The total answer by the process of round up

5. Find the surface area of the prism.
13 cm
5 cm
4 cm
12 cm

Answers

Answer:

162 sq. cm

Step-by-step explanation:

ph+ 2b

13 + 5 + 13 + 5 * 4 + 2 * 12

36 * 4 + 24

144 +24

168

Question 11(Multiple Choice Worth 1 points)

(08.06 MC)

The following data shows the weight, in pounds, of 5 boxes:

3, 1, 2, 2, 2

What is the value of the mean absolute deviation of the weight of the boxes, and what does it represent about the weight of a box?

(A.) 0.4 pound; on average, the weight of a box varies 0.4 pounds from the mean of 2 pounds

(B.) 0.8 pound; on average, the weight of a box varies 0.8 pounds from the mean of 2 pounds

(C.) 0.4 pound; the weight of 50% of the boxes is greater than 0.4 pound

(D.) 0.8 pound; the weight of 50% of the boxes is greater than 0.8 pound

Answers

Answer:

c is the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

First put the numbers from least to greatest: 1, 2, 2, 2, 3       2 is the mean.

Then you determine the distance each data value is from the mean.

1, 2, 2, 2, 3

1, 0, 0, 0, 1

Calculate the mean of the distances:  1 + 0 + 0 + 0 + 1 = 2

Then divide:  2 divided by 5 = 0.4

So your answer is 0.4 pound; on average, the weight of a box varies 0.4 pounds from the mean of 2 pounds

Select all the following that could
be the dimensions of a rectangular
prism with a volume 60 cubic
centimeters.

Answers

Answer:

A ; C ; D

Step-by-step explanation:

Volume of a rectangular prism:

V = l x w x h

1) 5 x 4 x 3 = 60 (ok)

2) 25 x 20 x 15. The result is > 60

3) 5 x 2 x 6 = 60 (ok)

4) 4 x 1 x 15 = 60 (ok)

5) 5 x 8 x 2 = 80

Solve using the tangent formula(real answers only please)

Answers

9514 1404 393

Answer:

  21.07

Step-by-step explanation:

The tangent ratio is ...

  Tan = Opposite/Adjacent

For the given values, this is ...

  tan(36°) = x/29

Solving for x, we have ...

  x = 29·tan(36°)

  x ≈ 21.07

Stephen opens a savings account with an initial deposit of $300.
Every month, Stephen will deposit an additional $250 into the
account from his paycheck. Which function below shows the total
amount of his deposits for x number of months?
A. y = 300x + 250
B. y = 12x + 550
C. y = x(300 + 250)
D. y = 250x + 300

Answers

D. Y=250x+300
For example let’s say Stephen has been doing this for 5 months
It would be 250(5)+ 300

WHATS X AND WHY URGENT !!!!!!

4x + 7.8y = 7.85
- 8x - y = -4.75

Answers

Answer:

X=.5, y=.75

Step-by-step explanation:

Answer:

x=0.5, y=0.75

Step-by-step explanation:

Method : Substitution Method

[tex]\begin{bmatrix}4x+7.8y=7.85\\ -8x-y=-4.75\end{bmatrix}\\\\[/tex]

Isolate in for 4x +7.8y=7.85 and solve

[tex]4x+7.8y=7.85\\\mathrm{Multiply\:both\:sides\:by\:}100\\\\4x\times\:100+7.8y\times\:100=7.85\times\:100\\\\Refine\\400x+780y=785\\\\\mathrm{Subtract\:}780y\mathrm{\:from\:both\:sides}\\400x+780y-780y=785-780y\\\\Simplify\\400x=785-780y\\\\\mathrm{Divide\:both\:sides\:by\:}400\\\frac{400x}{400}=\frac{785}{400}-\frac{780y}{400}\\\\Simplify\\x =\frac{157-156y}{80}\\\\\mathrm{Substitute\:}x=\frac{157-156y}{80}\\\\\begin{bmatrix}-8\times\frac{157-156y}{80}-y=-4.75\end{bmatrix}[/tex]

[tex]Simplify\\\\\begin{bmatrix}\frac{-157+146y}{10}=-4.75\end{bmatrix}\\\\Isolate\:y \:for \:\frac{-157+146y}{10}=-4.75\\\\\mathrm{Multiply\:both\:sides\:by\:}10\\\frac{10\left(-157+146y\right)}{10}=10\left(-4.75\right)\\\\-157+146y=-47.5\\\\-157+146y+157=-47.5+157\\\\Simplify\\146y=109.5\\\\\mathrm{Divide\:both\:sides\:by\:}146\\\frac{146y}{146}=\frac{109.5}{146}\\\\Simplify\\y=0.75\\\\\mathrm{For\:}x=\frac{157-156y}{80}\\\\\mathrm{Substitute\:}y=0.75\\\\x=\frac{157-156\times\:0.75}{80}\\\\x=0.5,\:y=0.75[/tex]

A(5, 23) and B(-2, 2) are two points.
(a) Find the co-ordinates of the midpoint of the line AB.​

Answers

Answer:

The midpoint of (5,23) and (-2,2) is (3/2,25/2)

hope that helps

Step-by-step explanation:

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