Let $z$ and $w$ be complex numbers satisfying $|z| = 5, |w| = 2,$ and $z\overline{w} = 6+8i.$ Then enter in the numbers \[|z+w|^2, |zw|^2, |z-w|^2, \left| \dfrac{z}{w} \right|^2 \]below, in the order listed above. If any of these cannot be uniquely determined from the information given, enter in a question mark. Don't even know where to start.

I got 49 for the first one, 100 for the second one, 9 for the 3rd one, and 6.25 for the 4th one. But it was wrong, so I don't know how to do this question.

Answers

Answer 1

Answer:

1st entry: 41

3rd entry: 17

Step-by-step explanation:

The 1st and 3rd entry are incorrect.

We will use the following for the 1st and 3rd:

[tex]|z+w|=|z|^2+|w|^2+2R(z\overline{w})[/tex]

[tex]|z-w|=|z|^2+|w|^2-2R(z\overline{w})[/tex]

where [tex]R(z\overline{w})[/tex] means 'real part of [tex]z\overline{w}[/tex]'.

Let's do part 1 now)

25+4+2(6)

29+12

41

Let's do part 3 now)

25+4-2(6)

29-12

17


Related Questions

2.
What is the slope of the line passing through the points (9,16) and
(3, 4)?

Answers

Answer:

2

Step-by-step explanation:

m = rise/run

m = (16-4) / (9-3)

m = 12 / 6 = 2

Is offering free credit on a new $30.000 car. You pay $3,000 down and then $900 a month for the next 30 months.

Answers

534 is the answer to this question.

Which points are solutions to the system of inequalities shown below?
Check all that apply.
y>x
y> 2
X>4
A. (6,4)
B. (4,2)
C. (8,1)
D. (9,-2)
E. (9, 10)
F. (5,6)

Answers

Answer:

F

Step-by-step explanation:

y should be greater than x and greater than 2.

x should be greater than 4 but less than y

what is the binomial expansion of (x+1)^5​

Answers

Answer: "A"

somewhat of a trick question

use pascals triangle (or binomial expansion)

0-1

1-1,1

21,2,1

3- 1,3,3,1

4- 1,4,6,4,1

5- 1,5,10,10,5,1

NOTICE THAT "A" has the 1,5,10,10,5,1  in the 5th row

Step-by-step explanation:

What is the circumference of a circle with a diameter of 9 inches? (use 22/7 for pi)

28 in.
24 in.
30 in.
27 in.

Answers

Answer:

28 inches

Step-by-step explanation:

The circumference is given by

C = pi *d

C = 22/7 ( 9)

C =198/7

    =28.28571429 inches

Pls help with this
Will give brainliest

Answers

Answer:

First one 2(x^2-4)

Like that you can do

Step-by-step explanation:

Vote as brainliest

Answer:

4(a). 2(x^2 - 4)

(e). ab(a^2 - b^2)

5(a). (x + 2)^2

(d). (x - 4)^2

6(a). -(3x - )^2

(b). 2(x-5)(x+5)

Step-by-step explanation:

If this helps you, please give brainliest!

What is 25% of 4kg 200g​

Answers

Step-by-step explanation:

25% of 4kg 200g

25/100 × 4.200

4.200/4

=1.05 kg or 1kg 50g

help asap ------------

Answers

Answer:

(-35, 0)

Step-by-step explanation:

x- intercept => y =0

y = -68, -51, -34, -17, 0

x = -79, -68, -57, -46, -35

(x, y) =>(-35, 0)

please help me which of the following is the quotient of the rational expressions shown below

Answers

Answer is C

✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔

The guy above me is correct it is c

What is the image point of (4, 6) after the
transformation T5,2 O ry=-x?

Answers

Answer:

The image point is (-1,-2)

Step-by-step explanation:

Firstly, we have to reflect the given point over the line y = -x after which we perform the translation using the coordinate (5,2)

Mathematically;

If we reflect a point (x,y) over the line y = -x

we have the coordinate change to (-y,-x)

so, (4,6) becomes (-6,-4)

Then for the translation, we add 5 to the new x-axis coordinate, then add 2 to the new y-axis coordinate

we have this as;

(-6 + 5, 2-4) = (-1,-2)

PQ and QR are 2 sides of a regular 12-sided polygon. PR is a diagonal of the polygon. Work out the size of angle PRQ. You must show your working.

Answers

Answer:

15°

Step-by-step explanation:

A regular polygon is a polygon in which all the sides and angles of the polygon are equal to each other.

A regular 12-sided polygon is a polygon with 12 equal sides and angles.

The sum of interior angles of a polygon is given as:

sum = (2n - 4)90; where n is the number of sides of the polygon

For a 12 sided polygon:

Sum of interior angles = (2 * 12 - 4)90 = (24 - 4)90 = 20 * 90 = 1800°

Therefore since all the angles are equal, each angle = 1800° / 12 = 150°

Therefore in the question, ∠PQR = 150° (angle of a 12 sided polygon), ∠PRQ = ∠QPR = x

Therefore in triangle PQR:

∠PQR + ∠PRQ + ∠QPR = 180°

150 + x + x = 180

150 + 2x = 180

2x = 30

x = 15°

∠PRQ = 15°

There are 1,281 souvenir paperweights that need to be packed in boxes. Each box will hold 15
paperweights. How many boxes will be needed?

Answers

Answer:

86 boxes

Step-by-step explanation:

Solve for x : 3(2x - 1) - (4-x) = 2(2x + 10 )

Answers

Answer:

6x-3-4+x=4x+20

7x-7=4x+20

7x-4x=20+7

3x=27

X=27/3

X=9

Answer:

(6×-3)-(-4+×)=4×+20

6×-3--4+×=4×+20

6×+1+×=4×+20

6×-4×=20-1

2×=19

devide by two both sides

×=9.5

Solve the problem.
An initial investment of $930 is appreciated for 19 years in an account that earns
6% interest, compounded continuously. Find the amount of money in the
account at the end of the period.
$1275.35
$22,067.28
$12,424,545.93
$2907.89

Answers

Answer:

$2907.89

General Formulas and Concepts:

Symbols

e (Euler's number) ≈ 2.71828

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra i

Compounded Continuously Formula: [tex]\displaystyle A = Pe^{rt}[/tex]

P is principle amountr is ratet is time

Step-by-step explanation:

Step 1: Define

Identify variables

P = 930

t = 19

r = 6% = 0.06

Step 2: Find Interest

Substitute in variables [Compounded Continuously Formula]:                    [tex]\displaystyle A = 930e^{19 \cdot 0.06}[/tex][Exponents] Multiply:                                                                                        [tex]\displaystyle A = 930e^{1.14}[/tex]Evaluate exponents:                                                                                         [tex]\displaystyle A = 930(3.12677)[/tex]Multiply:                                                                                                              [tex]\displaystyle A = 2907.89[/tex]

choose the equation of the line that is parrarel to the y axis

Answers

Hence, the equation of a straight line parallel to y-axis at a distance a from it is x = a. The equation of y-axis is x = 0, since, y-axis is a parallel to itself at a distance 0 from it. Let P (x, y) be any point on the y-axis. Then clearly, for all position of P we shall the same abscissa 0 or, x = 0.

the equation of a straight line is given as 3x+y=7. the slope of this line is​

Answers

Answer:

The slope is -3 and the y intercept is 7

Step-by-step explanation:

3x+y = 7

We can write the equation in slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = -3x+7

The slope is -3 and the y intercept is 7

The correct answer is -3

Find the missing side of the triangle and leave the answer in simplest radical form

Answers

Answer:

it would be radical 7

15 = x²+ 8

x²= 15 - 8

x²= 7 >>>>> radical 7 = x

Step-by-step explanation:

hope it helps

Answer:

x = √7.

Step-by-step explanation:

Using the Pythagoras theorem:

x^2 = (√15)^2 - (2√2)^2

x^2 = 15 - 8

x = √7.

In a standard deck of cards, there are 26 different red cards. How many possible combinations of 5 red cards
are there from those 26 cards?

Answers

Step-by-step explanation:

It doesn't matter what order they are drawn in, so youi have a combination problem

26C5

My calculator gives the answer directly,

It is 65780

PLEAAASE HELP!!! WILL GIVE BRAINLIEST!!!!!!

Answers

Answer:

Compared to a standard cosine function, the graph has a phase shift of [tex]5\pi/6[/tex] to the right, and compared to a sine function it has a phase of shift of [tex]\pi/6[/tex] to the right.

Step-by-step explanation:

The standard cosine function [tex]y=\cos x[/tex] has its maximum (vertex of the interval concave down) intersect with the y-axis. In this case, that part is shifted [tex]\frac{5\pi}{6}[/tex] to the right.

The standard sine function [tex]y=\sin x[/tex] has the point where it crosses its midline intersect with the x-axis. In this case, that part is shifted [tex]\frac{\pi}{6}[/tex] to the right.

find the area of the polygon.
I WILL MARK BRANIEST PLS ANSWER

Answers

Answer:

15cm^2

Step-by-step explanation:

The given polygon is a parallelogram,

Area of a parallelogram = Base * Height

                                       = 5cm * 3cm

                                       = 15cm^2

Hope it helped :)

the answer for this is 7.5

or when run becomes 8

Step by Step Explanation:

taken triangle KLM.

Area of a triangle=

[tex] \frac{1}{2} \times base \: \times height[/tex]

[tex] \frac{1}{2} \times 5 \times 3 \\ [/tex]

[tex] \frac{1}{2} \times 15[/tex]

= 7.5 or when run becomes 8

If the grain pile has a diameter of 60 feet and a height of 13 feet, what is the volume of the grain pile?


Answers

Answer:

36,738

Step-by-step explanation:

The first step is to calculate the radius

= 60/2

= 30

Therefore the volume can be calculated as follows

= πr^2h

= 3.142 × 30^2 × 13

= 3.14× 900×13

= 36,738 cubit feet

Hence the volume of the grain pile is 36,738 cubic feet

What is the slope of the line graph above?

Answers

This slope is 1/2. It goes up 1 on the y axis and over 2 on the x axis

−2(4y+1)=−8y−2??
Does it have one solution, no solution, or infinite?

Answers

Step-by-step explanation:

−2(4y+1)=−8y−2

4y+1=4y+1

infinite solutions

Answer:

Infinitely many solutions

Step-by-step explanation:

-2(4y+1)=−8y−2

=> -2(4y)-2(1)= -8y-2

=> -8y-2=-8y-2

=> Infinitely many solutions as x from both sides get cancelled

Devon needs to come up with ordered pairs that make up the line for this linear equation 3y - 3x =
12? Which ones would work?

Answers

Answer:

Step-by-step explanation:

The given linear equation can be reduced, ending up as  

y - x = 4   or   y = x + 4

If we choose our own x values, we can calculate the corresponding y value in each case:

x     y = x + 4    ordered pairs

0     4                (0, 4)

1      5                 (1, 5)

3      7                (3, 7)

-2     2                (-2, 2)

Solve 7x + 6 <3(x - 2).
A. {xlx>-3}
B. {xlx<-3}
C. {xlx<-2}
D. {x1x<0}

Answers

Answer:

x<-3

Step-by-step explanation:

if (x+y , 2x-3) = (5,3) find the value of x and y​. plz answer ASAP!!!

Answers

Answer:

x=3

y=0

Step-by-step explanation:

2x-3=3

2x=6

x=3

x+y=3

3+y=3

y=0

Answer:

ans: x= 3 and y= 2

Step-by-step explanation:

equating corresponding order pair,

x + y = 5 and

2x-3 = 3

so x=6/2 I.e

x= 3

putting x in

x + y = 5

y = 5- 3

y = 2

I have been stuck on this all day, please explain how to do this

Answers

Answer:$3,700

Step-by-step explanation:

Gross sales are the total amount of sales a company earned throughout a specific period of time, without taking into consideration any costs involved with running a business. Gross sales do not factor in expenses related to running a business, also known as cost of goods sold (COGS), which get deducted when calculating net sales. For example, they do not account for costs associated with item production, employee wages, building rent, returns, theft or sales tax.

Gross Sales = $3,700

Gross sales are the total amount of sales a company earned throughout a specific period that is 3700 dollars.

What is income tax?

Income tax is a tax applied on individuals or entities concerning income or profit earned by them.

Gross sales are the total amount of sales a company earned throughout a specific period, without taking into consideration any costs involved with running a business.

Gross sales do not factor in expenses related to running a business, also known as cost of goods sold (COGS), which get deducted when calculating net sales.

For example, they do not account for costs associated with item production, employee wages, building rent, returns, theft, or sales tax.

Gross Sales = $3,700

Learn more about sales;

https://brainly.com/question/15375944

#SPJ2

How can you add eight 4s together so that the total adds up to 500?

Answers

You can also multiply the 8 4s like 8x4 but it won’t add up to 500

Need help of this!! Domain and range!!

Answers

Answer:

its the first one

Step-by-step explanation:

It’s the last one because the domain is x/x is greater than or equal to -4 and the range is y/y is greater than or equal to 0

If a + b = 5 and a - b = 9, what is a^2+b^2?

Answers

Answer:

=53

Step-by-step explanation:

a=5-b     &.    a=9+b

combine

5-b=9+b

-4=2b

b= -2

thus, a=7

(-2)^2 + (7)^2

4+49

=53

Mark Brainliest please

Answer : 3²+2²=13.

Step-by-step:

Ok …according to the question

a+b=5–(1)considering it as eqn 1

a-b=9—(2)considering it as eqn 2

Substracting eqn 2 from eqn 1 we get

2b=4

b=4/2

b=2

Now substituting this value of b in eqn 1 we get

a+2=5

So a=5–2

a=3

So a=3and b=2
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