Two complex numbers are represented by c + d[tex]i[/tex] and e-f[tex]i[/tex] , where c, d, e, and f are positive real numbers. In what two quadrants may the product of these complex numbers lie? Explain your answer in complete sentences.

Answers

Answer 1

Answers: First Quadrant and Fourth Quadrant

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

Explanation:

Let

w = c + diz = e - fi

be the two complex numbers.

Multiply them out to see what we get

[tex]w*z = (c+di)(e-fi)\\\\w*z = c(e-fi)+di(e-fi)\\\\w*z = ce-cf*i+de*i-df*i^2\\\\w*z = ce-cf*i+de*i-df*(-1)\\\\w*z = ce-cf*i+de*i+df\\\\w*z = (ce+df)+(-cf+de)*i\\\\[/tex]

The result we get is in the form a+bi where

a = ce+df = real partb = -cf+de = imaginary part

Recall that any complex number of the form a+bi can be plotted on the xy plane with 'a' being treated as the x coordinate and b as the y coordinate. In short, the location of a+bi is at the point (a,b)

With c,d,e,f being positive, this means ce and df are positive, and a = ce+df is also positive.

This places the result of wz in either the first or fourth quadrants (the northeast or southeast quadrants respectively), due to the positive x coordinate.

We don't have enough info to determine whether b = -cf+de is positive or not. So that's why we can't nail down the precise quadrant of wz

If b > 0, then wz is in quadrant 1

If b < 0, then wz is in quadrant 4


Related Questions

cos 0 = 12/13. Find sin 0.
A. 5/12
B. 12/5
C. 13/12
D. 5/13

Answers

The correct value of Sine θ is 5/13

From the question given above, the following data were obtained:

Cos θ = 12/13

Sine θ =?

Next, we shall determine the opposite. This can be obtained as follow:

[tex]Cos \theta = \frac{Adjacent}{Hypothenus}\\\\Cos \theta = \frac{12}{13}[/tex]

Adjacent = 12

Hypothenus = 13

Opposite =?

Hypothenus² = Opposite² + Adjacent²

13² = Opposite² + 12²

169 = Opposite² + 144

Collect like terms

169 – 144 = Opposite²

25 = Opposite²

Take the square root of both side

Opposite = √25

Opposite = 5

Finally, we shall determine the Sine θ. This can be obtained as follow:

Opposite = 5

Hypothenus = 13

Sine θ =.?

[tex]Sine\theta = \frac{Opposite}{Hypothenus}\\\\Sine\theta = \frac{5}{13}[/tex]

Therefore, the value of Sine θ is 5/13

Learn more: https://brainly.com/question/23699928

Answer:

D. 5/13

Step-by-step explanation:

5f - 2g + 3f - 4 - g

Answers

Answer:

8f-3g-4

Step-by-step explanation:

hope this helps U0U

A car travels a distance of 350 km in a time of 5 hours.
What is the car's average speed?

Answers

Answer:

answer is 70 km/h

OR,

19.44 m/s

Step-by-step explanation:

if a right triangle has legs that are 7 and 24 what is the length of the hypotenuse

Answers

Answer:

25

HOPE THIS HELPS

- Todo ❤️

Step-by-step explanation:

7^2=49

24^2=576

576+49=625

Sqrt 625=25

A square pyramid with a height of 7 inches has a volume of 47.25 cubic inches. Find the side length of the square base.
The side length is inches.

Answers

Answer:

4.5 inches

Step-by-step explanation:

volume= 1/3 (base area) × height

47.25= 1/3 ( base area) × 7

20.25 = base area

now since the base is a square we can evaluate base area = length²

20.25= length²

length = 4.5 inches

There are 60 players on a football team. 2/3 of the players are offensive team players 1/12 of the players are special team players The reaming players are defensive players. Each team member is either an offensive, defensive, or special team player. The number of defensive players is -

Answers

Answer:

15

Step-by-step explanation:

2/3 x 60 = 40

1/12 x 60 = 5

60 - 40 - 5 = 15

PLEASE PLS HELP THANK YOU

x = ___ cm

Answers

Answer:

x = 7

Step-by-step explanation:

5/(40+5) = 3/(2x+10+3)

1/9 = 3/(2x+13)

2x+13 = 3×9

2x = 27 - 13

x = 14/2

x = 7

Answer:

Step-by-step explanation:

Since they are directly proportional:

5cm -> 3cm

40cm -> y

y = 120/5

 = 24cm

2x+10 = 24

2x = 14

x = 7cm

Feel free to mark it as brainliest :D

If 2x + 4 = 10. What is the value of x

Answers

Answer:

x=3

Step-by-step explanation:

You subtract the 4 from +4 d +10 and then you left with 2x=6

Then you divide the numbers both by 2 so you are left with x=3.

Have a nice day!!!!!!!!!!

Answer:

x=3

Step-by-step explanation:

2x + 4 - 4 = 10 - 4

2x ÷ 2 = 6 ÷ 2

x = 3

Help me with the question​

Answers

Answer:

Step-by-step explanation:

Is the purple triangle a right triangle? Explain.

Answers

Answer:

yes it has a right angle

Step-by-step explanation:

If your class received a new student today, describe how you would teach the new student to perform the 90 degrees clockwise rotation of the blue preimage to get the red image.

Answers

You would tell him to turn around it’s pretty easy

The area of a triangle is 36 4 5 units squared and the height of the triangle is 9 1 5 units. What is the length of the triangle's base?

Answers

Answer:

I think it should be somewhere around 3528.3

Step-by-step explanation:

this is because 3645 squared minus 915 squared is 12448800 and the square root of that is 3528.3 I could be wrong though but just trying to help

(8x10^-3)+(2 x 10^-4)​

Answers

Answer:

0.0082

Step-by-step explanation:

You spin the spinner once.
What is P(3)?

Answers

Answer:

You spin the spinner once. What is P(3)? Answer : 8%.

Evaluate: f(2) =
Helpppp

Answers

Answer:

32

Step-by-step explanation:

What is the greatest common factor of 50, 40, and 20?

Answers

Answer:

10

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

The gcf is 10

Step-by-step explanation:

Morgan invested $1,200 in an account that pays 6% annual simple interest. Morgan will not make any additional deposits or withdrawals. How much interest will Morgan earn on her investment at the end of 7 years?

Answers

Answer:

Step-by-step explanation:

Simple interest per year = $17,500 (0.0825) = $1,443.75 Simple interest = $8,662.50 Joseph Harris is considering an investment that pays 6.5 percent annually

Find the indicated term in the sequence.

Please show steps too! Thank you.

Answers

Answer:

Value of An if n is 17 = -834

Step-by-step explanation:

Given:

A100 = 245

d = 13

n = 17

Find:

Value of An if n = 17

Computation:

An = a + (n-1)d

A100 = a + (100-1)13

245 = a + (99)17

245 = a + 1,287

a = 245 - 1,287

a = -1,042

So,

Value of An if n = 17

An = a + (n-1)d

A17 = -1,042 + (17-1)(13)

A17 = -1,042 + (16)(13)

A17 = -1,042 + 208

A17 = -834

Value of An if n is 17 = -834

Randy has 36 tiles.
How should he arrange them so that he has the smallest perimeter?
A.

4 by 9 rectangle
B.

3 by 12 rectangle
C.

1 by 36 rectangle
D.

6 by 6 rectangle

Answers

Answer:

Smallest perimeter setup is (6 by 6 rectangle)

Step-by-step explanation:

Given:

Total number of tile = 36

Find:

Smallest perimeter setup

Computation:

Perimeter = 2(a + b)

So,

Perimeter if (4 by 9 rectangle )

Perimeter if (4 by 9 rectangle ) = 2[4+9]

Perimeter if (4 by 9 rectangle ) = 2[13]

Perimeter if (4 by 9 rectangle ) = 26

Perimeter if (3 by 12 rectangle )

Perimeter if (3 by 12 rectangle ) = 2[3+12]

Perimeter if (3 by 12 rectangle ) = 2[15]

Perimeter if (3 by 12 rectangle ) = 30

Perimeter if (1 by 36 rectangle )

Perimeter if (1 by 36 rectangle ) = 2[1+36]

Perimeter if (1 by 36 rectangle ) = 2[37]

Perimeter if (1 by 36 rectangle ) = 74

Perimeter if (6 by 6 rectangle )

Perimeter if (6 by 6 rectangle ) = 2[6+6]

Perimeter if (6 by 6 rectangle ) = 2[12]

Perimeter if (6 by 6 rectangle ) = 24

So,

Smallest perimeter setup is (6 by 6 rectangle)

The function y=15,000(1.10)xmodels the cost of annual tuition at a local college, x years after 2000. How much will tuition be in 2025?

Answers

Answer: [tex]162,520.588[/tex]

Step-by-step explanation:

Given

The function [tex]y=15,000(1.1)^x[/tex] models the cost of tuition fees after year 2000

In year 2025 that is 25 years after 2000, fees can be given as

[tex]\Rightarrow y=15,000(1.1)^{25}\\\Rightarrow y=15,000\times 10.834\\\Rightarrow y=162,520.588[/tex]

Thus, the fees in year 2025 is [tex]162,520.588[/tex].

Which symbol correctly compares the two angle measures?
radians
60°
A. =
B. <
C. >

Answers

Answer:

Is B

Step-by-step explanation:

Nine times a number, subtracted from the square of the number, is 36. Find the two numbers.

Answers

Answer:

- 3 and 12

Step-by-step explanation:

let n be the number , then

n² - 9n = 36 ( subtract 36 from both sides )

n² - 9n - 36 = 0

Consider the factors of the constant term (- 36) which sum to give the coefficient of the n- term (- 9)

The factors are - 12 and + 3 , since

- 12 × 3 = - 36 and - 12 + 3 = - 9 , then

(n - 12)(n + 3) = 0

Equate each factor to zero and solve for n

n - 12 = 0 ⇒ n = 12

n + 3 = 0 ⇒ n = - 3

The 2 numbers are - 3 and 12

hey! i’ll give brainliest please help

Answers

Answer:

insects adapted for stronger flight may survive in greater numbers.

D is your answer. The forth one down.

hey! please help i’ll give brainliest

Answers

Answer:

Heyo! the answer is A since their implying it's important :)

Each of 2 boxes of markers held 6 markers. Each of 3 packs of
rulers held 4 rulers.
How many markers and rulers were there altogether?

Answers

CORRECT ANSWER: 16 markers, 12 Rulers

EXPLANATION:
2 * 6 = 12
3 * 4 = 12

What is 6.27 in expanded form?

Answers

Answer:

6+0.2+0.07

hope this helps

have a good day :)

Step-by-step explanation:

If the weight of a package is multiplied by 3/7 the result is 42 pounds. Find the weight of the package.

Answers

Answer:

B

Step-by-step explanation:

x*3/7=42

divide 42 by 3/7: 42*7/3=98

x=98

Answer:

B) 98

Step-by-step explanation:

3/7 = 42/x

3x = 294

x = 98

Mrs.Taylor has cards labeled with rational numbers. *Three cards are labeled -6.35 *One card is labeled -7.53 *Two cards are labeled 8.31 What are the average numbers on the cards? *please help me on this!!*

Answers

Answer:

about 1.18 is the closest is what i got

Step-by-step explanation:

Determine the measures of A, B, C and D.

Answers

Answer:

[tex]\angle A = 32 \deg[/tex]

[tex]\angle B = 105 \deg[/tex]

[tex]\angle C = 94 \deg[/tex]

[tex]\angle D = 138 \deg[/tex]

which two decimals have the same value as 7/10 ​

Answers

Answer:

B and C

Step-by-step explanation:

they're the same butthe other one has 0 at the end which doesn't really change anything from .7

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