Mathematics High School

prove the indicated operations.
(3-i)(4+3i)(5-2i)

Answers

Answer 1

Answer:

I hope if one of these help.

Step-by-step explanation:

(4 - 3i) + (2 + i )(5 - 2i)

=16 - 2i

If you simplify your answer will be: 16−2i

1) (3+2i)-(1-6i)

2) 4i+3-6+i-1

3) 5i(3-2i)

4) (5+3i)(2-3i)

5) (2+i)(2-i)

1) (3 + 2i) - (1 - 6i)

 3 + 2i - 1 + 6i

 2 + 8i

2) 4i + 3 - 6 + i - 1

  5i - 3 - 1

  5i - 4

3) 5i ( 3 - 2i )

  15i - 10i^2

  15i - 10 ( -1 )

  15i + 10

4) ( 5 + 3i ) ( 2 - 3i )

  10 - 15i + 6i - 9i^2

  10 - 9i - 9i^2

  10 - 9i - 9 ( -1 )

  10 - 9i + 9

 - 9i + 19

5) ( 2 + i ) ( 2 - i )

   4  - 2i + 2i - i^2

   4 - i^2

   4 - (-1)

   5

1) 2 + 8i

2) -4 + 5i

3) 10 + 15i

4) 19 - 9i

5) 5

The operations with imaginary numbers are equal to those of the real numbers considering i as a variable, but with a property that allows to simplify the expression more, that is that i squared equals -1. Taking this property into account, we solve the expressions like this:

1) (3 + 2i) - (1-6i) = 3 + 2i - 1 + 6i = 2 + 8i

2) 4i + 3-6 + i-1 = 5i - 4 = -4 + 5i

3) 5i (3-2i) = 5i*3 - 5i*2i = 15i - 10i^2 = 15i - 10(-1) = 15i + 10 = 10 + 15i

4) (5 + 3i) (2-3i) = 5*2 - 5 3i + 3i*2 - 3*3i^2 = 10 - 15i + 6i - 9i^2 = 10 - 9i - 9(-1) = 10 - 9i + 9 = 19 - 9i

5) (2 + i) (2-i) = 2*2 - 2*i + 2*i - i^2 = 4 - 2i + 2i - (-1) = 4 + 1 = 5

I hope one of these help:)

Related Questions

what is a multiple of 12h^3?

Answers

Answer:

3.49099569 × 10-99 m6 kg3 / s3

Step-by-step explanation:

How old am I if 400 reduced by 3 times
my age is 181?

Answers

You would be 73. 400-(your age*3)=181

Answer:

45

Step-by-step explanation:

tables originally priced at $70 are now on sale for $42.What is the discount, as a percentage?​

Answers

Answer:

40%

Step-by-step explanation:

you saved $28.00

Select the fraction that is NOT in lowest terms . which of these fractions is not in lowest term?

3/14
15/23
10/63
14/21

Answers

Answer:

14/21

Step-by-step explanation:

14/21 is divisible by 7, and can reduce to 2/3

Si la temperatura de un día de invierno esta en 6°C y baja 10°C, ¿cuanto marcara el termómetro?

Answers

Answer:

el termómetro sería de 4 grados Celsius negativos

Step-by-step explanation:

¡Espero que esto ayude!

A scarf cost $17 after the 15% discount was applied. What is the original price?

Answers

the correct answer is $20!!!

20-15%= 17

find the area of the triangle​

Answers

Answer:

area = ½bh

= 1/2×11× 15

= 82.5 Square inches

82.5 Square InchesStep-by-step explanation:15x11/2 = 82.5

Mhanifa please help with this I want to pass! I will mark brainliest! I will report random answers

Answers

Answer:

Questions 1 and 3 already answered

Q2

Angles 1 and 3 are corresponding angles and therefore have same value:

4x = 112x = 112/4x = 28°

need help with this if anyone could help thanks

Answers

its the third answer choice

What are the ordered pairs are the solutions for the following system of equations??

Answers

Answer:

(1,2) and (6,7)

Step-by-step explanation:

The ratio of cats to dogs is 3 : 7.
12 dogs escaped and the ratio is now 3 : 4.
Work out how many animals there were at the beginning.

Answers

Given:

The ratio of cats to dogs is 3:7.

12 dogs escaped and the ratio is now 3 : 4.

To find:

The total number of animal at the beginning.

Solution:

Let the number of cats and dogs at the beginning are 3x and 7x respectively.

12 dogs escaped. So, the remaining number of dogs is (7x-12).

New ratio of cats and dogs is 3:4.

[tex]\dfrac{3x}{7x-12}=\dfrac{3}{4}[/tex]

[tex]4(3x)=3(7x-12)[/tex]

[tex]12x=21x-36[/tex]

[tex]12x-21x=-36[/tex]

[tex]-9x=-36[/tex]

Divide both sides by -9.

[tex]\dfrac{-9x}{-9}=\dfrac{-36}{-9}[/tex]

[tex]x=4[/tex]

Now, the total number of animals at the beginning is

[tex]Total=3x+7x[/tex]

[tex]Total=10x[/tex]

[tex]Total=10(4)[/tex]

[tex]Total=40[/tex]

Therefore, the total number of animals at the beginning is 40.

FOR 20 POINTS:
What expression is represented in the model shown below?

Answers

Answer:

I can't see the picture

Step-by-step explanation:

In each of the following graphs, the two given polygons are similar. Write precisely a single dilation (coordinates of center and coefficient) by which the image (labeled with primed letters) was obtained. Will Give Brainiest!!!!!

Answers

Answer:

Center: (0,0)   coefficient: [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

The side of the smaller polygon is 1/3 the size of the larger one, and that is why the coefficient is 1/3.

Polygon MNPQ was dilated by a scale factor of 1/3 and center of dilation (0, 0) to create M'N'P'Q'.

What is dilation?

Dilation is the increase or decrease in the size of a figure by a scale factor of k, thereby creating an image.

From the diagram:

Scale factor = N'P' / NP = 2/6 = 1/3

Center = (0, 0)

Polygon MNPQ was dilated by a scale factor of 1/3 and center of dilation (0, 0) to create M'N'P'Q'.

Find out more on dilation at: https://brainly.com/question/10253650

90 + 90 ÷ 90 = _________​

Answers

Answer:

91

Step-by-step explanation:

this is correct answer

Answer:

91

Step-by-step explanation:

Using BODMAS,

90 + (90/90)

=> 90 + 1

=> 91

Find the missing angle

Answers

Answer:

110 Degrees

Step-by-step explanation:

Every interior triangle equalls 180 degress. So you subtract what you already have from 180.

30+40+x=180

70+x=180

180-70=110

A triangle is always equals to 180 so you have to do:
40+30=70
180-70=110
F=110°

Tom has 50 coins consisting of quarters and dimes. The combined value of coins is $8.30. How many dimes and quarters does Tom have:
dimes
quarters

Answers

Answer:

thirty two quarters and three dimes

HELP.
What is the best bat All-Time?
-Quatro Pro
-The Goods (2021)
-Marucci 5,6,7
-Voodoo Liquidmetal, etc.
-Other (comment)

Answers

Answer:

Easton Redline Sc500

That is the best bat at all time

Step-by-step explanation:

I WILL GIVE BRAINLIST NEED HELP ASAP
Find the volume of this rectangular prism in cubic inches
A
3 cubic inches
B
36 cubic inches
C
5,184 cubic inches
D
46,656 cubic inches

Answers

Answer:

A

Step-by-step explanation:

2 X 1.5 X 1 = 3

Answer:

a

Step-by-step explanation:

loook below giving brainliest

Answers

To find the Surface area of a prism, we need to calculate the sum of the area of each of the shapes that make up the net of the object.

(11 x 15 x 2) + (5 x 15 x 2) + (5 x 11 x 2)

= 590ft ^2

Hope this helps!!

PKZ HELP AND EXPLAIN!!! WILL GIVE BRAINLY

Answers

Answer:

The graph shown has a slope of -4 (the line goes up 4 units for every 1 unit traveled to the left)

The y-intercept (where the line crosses the y axis) is -3

Slope-intercept form is y=mx+b

(m=slope)

(b= y-intercept)

Therefore, your answer would be y=-4x-3

Step-by-step explanation:

Line t has slope 3/4 and passes through (0, 0) . Follow these steps:Step
1: Start at (0, 0) Step
2: Move right 8 units​

Answers

Answer:

(8,0)

Step-by-step explanation:

y=mx+b

0=(3/4)0+b

0=b

y=3/4x+0

the point eight units away from (0,0)

is (8,0)

Hope this helps :)

I am building birdhouses for all of my students for an upcoming project. If I complete 2 1/2 birdhouses in 2/3 of an hour of workwhat is my unit rate of birdhouses per bour?

Answers

Answer:

3 3/4

Step-by-step explanation:

convert to decimal

2.50/0.666

=3.75

Seventh grade > L.8 Solve percent equations: word problems JS6
Harold's Diner offers its clients a choice of regular and diet soda. Last night, the diner served
40 sodas in all, 10 of which were regular. What percentage of the sodas were regular?

Answers

30% diet and 10 regular not shoreee

What is the awnser to pie
A. 3.14195
B. 4.0238
C. 5.3843
D. 6.2322

Answers

Answer:

A

Step-by-step explanation:

Need help again will give the brainliest

Answers

The answer is 840 cm2

oscar debe encontrar el valor de m en la ecuación -2(m+6m)-6=-4(m+6)-4m para poder encontrar el equilibrio de una balanza cuál es el valor de m

Answers

Answer:

sorry error bessssssssss

Find the measure of < FGE.
please provide step by step equation

Answers

Answer: 62 degrees

Step-by-step explanation:

.130-180=50

.16x+4+14x+6+50=180

.180-4-6-50=120

.16x+14x=120

.30x=120

.x=4

.14(4)+6

.56+6

.62

Choose Yes or No to tell if the fraction 4/9 will make each equation true.

Answers

1. Yes
2. Yes
3. No
4. Yes

Answer:

Step-by-step explanation:

1) yes

2)yes

3)no

4)yes

i hope it help because all you gotta do is just multiply all the numbers by 4,9

Answer ASAP pls pls

Answers

D be the correct answer

Heather drew the scaled drawing of a train car shown below. She used the scale of 2 cm = 5 ft to complete the
drawing.
Train Car
10.8 cm
What is the actual length of the train car?
A.21.6 ft
B.27 ft
C.43.2 ft
D54 ft

Answers

Answer: c

Step-by-step explanation:

The required actual length of the train is given as 27 ft.

Given that,
Heather drew the scaled drawing of a train car shown below. She used the scale of 2 cm = 5 ft to complete the drawing.

What is the scale factor?

The scale factor is defined as the ratio of the modified change in length to the original length.

here,
As given,
2 cm = 5 ft
1 cm = 5/2 ft
Tain car length = 10.8 m
Actual length = 10.8 × 5/2 = 27 ft

Thus, the required actual length of the train is given as 27 ft.

Learn more about Scale factors here:

https://brainly.com/question/22312172

#SPJ1

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