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

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

Answers

Answer:

I can't see the picture

Step-by-step explanation:

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

Answers

the correct answer is $20!!!

20-15%= 17

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

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

what is a multiple of 12h^3?

Answers

Answer:

3.49099569 × 10-99 m6 kg3 / s3

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:

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:

Need help again will give the brainliest

Answers

The answer is 840 cm2

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:

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.

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

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°

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:

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:

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

need help with this if anyone could help thanks

Answers

its the third answer choice

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!

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!!

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

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

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

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:

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

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

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

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 :)

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°

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

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

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