Simplify the expression to a + bi form: (10 + 6i)(- 2 - 4i)

Answers

Answer 1
Answer:

[tex] \Large{\boxed{\sf (10 + 6i)(-2 - 4i) = 4 - 52i}} [/tex]

[tex] \\ [/tex]

Explanation:

To find the algebraic form, also called 'a + bi form', of the given complex number, we will have to expand its expression using FOIL method.

[tex] \\ [/tex]

[tex] \Large{ \sf \: \underline{FOIL \: method \text{:}}} \\ \\ \Large{\boxed{\sf (A + B)(C + D) = AC + AD + BC + BD}} [/tex]

[tex] \\ [/tex]

Let's identify our coefficients and expand the given expression:

[tex] \sf (\underbrace{\sf 10}_{A} + \overbrace{\sf 6i}^{B})(\underbrace{\sf -2}_{C} \overbrace{\sf -4i}^{D}) = 10 \times (-2) + 10 \times (-4i) + 6i \times (-2) + 6i \times (-4i) \\ \\ \\ \sf = -20 - 40i - 12i - 24i^2 = -20 - 52i - 24i^2 [/tex]

[tex] \\ [/tex]

In the complex number system, i² = -1. Therefore, our final answer is:

[tex] \sf (10 + 6i)(- 2 - 4i) = -20 - 52i - 24(-1)= \boxed{\boxed{\sf 4 - 52i}} [/tex]

[tex] \\ \\ [/tex]

▪️Learn more about the algebraic form of a complex number here:

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Related Questions

increase £40 by 35% =

Answers

Answer:

£54

Step-by-step explanation:

An increase of 35% on the original 100% is 100% + 35% = 135% = 1.35 , so

1.35 × £40 = £54

Which of the following is not true?


p+q = q+p
p x q = q x p
p x (q x r)=(p x q ) x r
p - q = q - p



Plz answer my exam is going on right now

Answers

Step-by-step explanation:

the number 4 is false

p-q =-(q-p)

solve please :3 will mark brainliest !!

Answers

>> Answer

__________

[tex] \: [/tex]

6f = $15

8f = $20

10f = ?

Soo :

2f = 5

f = 2,5

10f = 10(2,5) = $25

The cost of the wire of the third length in the table is, 25 dollars

We have to give that,

The cost of a certain type of wire varies directly with its length.

Now, From the table the equation between cost and length is,

y - 15 = (20 - 15)/(8 - 6) (x - 6)

y - 15 = (5/2) (x - 6)

y - 15 = 2.5x - 15

y = 2.5x

Where y represents the cost and x represent the length.

Hence, At x = 10 feet

y = 2.5 (10)

y = 25 dollars

So, The cost of the wire is, 25 dollars

To learn more about the equation visit:

brainly.com/question/28871326

#SPJ6

please help me or I'm gonna fail math​

Answers

Answer:

length = x+6

width = x-6

Step-by-step explanation:

The area of rectangle is:

[tex] \displaystyle \large{ A= l \times w}[/tex]

where A is area, l is length and w is width.

We know the area of this rectangle or table since we are given A = x^2-36.

First, substitute A = x^2-36 in.

[tex] \displaystyle \large{ {x}^{2} - 36 = lw}[/tex]

Then we factor x^2-36, use the difference of two squares:

[tex] \displaystyle \large{ (x + 6)(x - 6) = lw}[/tex]

Compare the terms.

First, we have to understand that length is always longer or greater or have more values than width.

Hence length cannot be x-6 and width cannot be x+6 either.

Thus:

[tex] \displaystyle \large{length = x + 6} \\ \displaystyle \large{width = x - 6}[/tex]

James wants to buy a new cell phone package. There are three packages available, each offering a different deal.Package 1$160 for 4 monthsPackage 2$128 for 4 monthsPackage 3$60 for 2 monthsWhich package offers the best deal?A.Package 3B.Package 1C.Package 2D.Both Package 1 and Package 2

Answers

Answer:

to get which one is the best we have to bring them packages to the same terms

so to do that we have to find what each package offers per month by divided the amount by the number of months

so

160/4= 40

128/4=32

60/2=30

so the best package is

B. package 1

Simplify the expression. -17+[(8-3)-(-14-19)]=

Answers

Answer:

21

Step-by-step explanation:

trust (used a calculator)

if 3^x = 1, find the value of x.​

Answers

3x-1=?

maybe 3x-1=5

3x=5+1

3x=6

X=6/3

X=2

[tex]\sf x-12=14[/tex]

Answers

Answer:

X - 12 = 14
+12. +12

X = 26

6. Cafe A offers 2 free bottled waters or juices for every 20 purchased. What is the ratio of free drinks to purchased drinks? *

Answers

Answer:

1: 10

Step-by-step explanation:

2/2 =2

20/2 = 10

What do all similar circles have in common?

Answers

Answer:

Explanations (4) Similarity is a quality of scaling: two shapes are similar if you can scale one to be like the other, like these triangles ABC and DEF. Since all circles are of the same shape (they only vary by size), any circle can be scaled to form any other circle. Thus, all circles are similar!

Step-by-step explanation:

Welcome


So, if the average family earned $4,000 per month, how much would they send back
out to pay debreach month
What kinds of things could you do with that money?

Answers

hazlo tu misma, perra. buy

Simplify the expression to a + bi form:
(11 + 9i)2

Answers

Answer:

22+18i

Step-by-step explanation:

distribute the 2

22+18i

To find out how fast a tree grows, you can measure its trunk. A giant red oak's diameter was 248 inches in 1965. The tree's diameter had grown to 251 inches in 2005. Find the average rate of change in the diameter of the tree per year.


CLEAR CHECK

1313 inches per year


-0.075 inch per year


0.075 inch per year


3 inches per year

Answers

I think it's 0.075 inch per year

Answer:

Your answer is C. or 0.075 inches per year.

Step-by-step explanation:

251-248 = 3 ( To figure out how much it grew )

2005 -1965 = 40   ( To figure out how long it took )

3/40 = 0.075

PLEASE HELP ME I REALLY NEED ITTT

Answers

Answer:

bru you have a head

Step-by-step explanation:

use ittt

pls help!!!!!!! i will give brainliest!!!!!

Answers

Answer:

There is a strong positive correlation

Step-by-step explanation:

The graph shows as more students study the higher the test score is.

i need some frikin help on equations like this 4x>2 i used to do questions like this 4x=2 (basically one step equations) im just really confused

Answers

Answer:

x>1/2

Step-by-step explanation:

4x>2

4x/4

2/4

x>2/4

2/4 divided by 2= 1/2

x>1/2

I need help with a and b!

Answers

Answer: first a it’s left side is shorter while on the other polygoes there left sides longer for the first two

in the third one it goes size wise

Step-by-step explanation:

Find the area and perimeter of
the parallelogram:
17ft
12ft
15ft

Answers

Step-by-step explanation:

The area = base × height

= 12 × 17 = 204

the perimeter = 2(17 + 15) = 2 × 32 = 64

please give me a brainliest answer

SOMEONE PLEASE HELP AND SHOW WORK i will give you brainliest!
Katy invests a total of $26,500 in two accounts. The first account earned a rate of return of 15% (after a year). However, the second account suffered a 8% loss in the same time period. At the end of one year, the total amount of money gained was $985.00. How much was invested into each account?

Answers

Answer:

Step-by-step explanation:

0.15x-0.08(26,500-x)=98.00

15x-212000+8x=98,500

23x+212000=98,500+212000

23x/23= 310500/23

x = 13500 (was invested in the account that gained 15% )

26500-13500=13000 (was invested in the account that lost 8%.)

HELP PLEASE I DON´T UNDERSTAND RATIOS!

Answers

Answer:

Jake made 7 bead strings

Step-by-step explanation:

The ratio is 2:6 next would be 4:12 then 6:18 and so on. You just add what you started with to the corresponding side. 8:24, 10:30, 12:36, 14:42. The right side is 3x the left side.

Answer:

Step-by-step explanation:

You don't really need to use ratios for this question. You need to understand that for each necklace he uses 2 red and 6 whites.

Let the number of necklaces he can make = x

The total number of beads = 56

2x + 6x = 56

8x = 56                     Divide by 8

8x/8 = 56/8

x = 7

So the number of necklaces possible is 7.

If you insist on doing this with ratios then you could do it as

2/8 = x/56   What this means is that 2 reds to the total = x / 56. The 56 is the total number of beads used. The x represents the number of reds.

2/8 = x/56                         Cross multiply

2 * 56 = 8x                        Divide both sides by 8

2 * 56/8 = x

x = 14.

That means of the 56 beads used, 14 of them are red.

6/8 = y / 56                      Cross multiply

6*56 = 8y

336 = 8y                           Divide by 8

336/8 = 8y/8

y = 42

This means that 42 beads were white

 The total is 56. But here's the catch. The highest prime common to both is 7 and that's how many necklaces can be made.

The distributive property simplify each expression. Question 3. 3(4+3r)

Answers

Answer:

12 + 9r

Step-by-step explanation:

3(4 + 3r)

= 12 + 9r

Answer:

12 + 9r

Step-by-step explanation:

just multiply 3 by 4 and then 3r.


Subtract 2y - 3 from 8y-2.

Answers

Answer:

2(3y-2)

Step-by-step explanation:

Collect like terms

6y-4

Simple terms

2(3y-2)

$300, 5%, 2 years

explain

Answers

ANSWER:16,000

EXPLANATION:

300+5%+2YEARS=16,000

HOPE IT HELPS YOU

CAN YOU BRAINLEST ME

Answer:

16,000

Step-by-step explanation:

trust me it's right

Donna bought 4 bags of dog treats for $10.72. What is the cost per bag of dog treats?

Answers

Answer:

2.68

Step-by-step explanation:

Answer: The bags cost about $2.68 each

Step-by-step explanation: All I did was simple Division: ($10.72 ÷ 4 = $2.68) If you need to double check to see if this is accurate, you can do ($2.68 x 4= 10.72)  Therefore, this equation has an accurate answer.~

Hope this helps, have a great day/night!

~IFoundJiminsLostJams~

WILL GIVE BRAINLIEST

solve for x : -4 = (2/3)x

show steps please

Answers

Answer:  x = -6

Step-by-step explanation:

To solve for x, we have to find a way to make x the subject of the equation (get x on one side and everything else on the other side)

since    -4 = (2/3)x     [mutiply both sides by 3]

⇒    -4 × 3 = 2x     [divide both sides by 2]

⇒   (-12/2) = x      [simplify by dividing -12 by 2]

∴            x = -6

Answer:

X = 6

Step-by-step explanation:

2/3 x 6/1 = 4

2 x 6 = 12

3 x 1 = 3

12/3 = 4

12 divided by 3 is 4

The answer is 6 , x = 6

please help I dont understand​

Answers

Answer:

3rd option

Step-by-step explanation:

A direct variation is expressed in this form:

y = kx

1. y - 4x = 8

y = 4x + 8 is not a direct variation

2. y + 2 = 7x

y = 7x - 2 is not a direct variation

3. y - 3x = 0

y = 3x is a direct variation

4. y = 5x - 2

y = 5x - 2 is not direct variation

3|-d + 2| + 1 if d = 4

Answers

Answer:

7

Step-by-step explanation:

reminder that the absolute value function always gives a positive result.

3 | - d + 2 | + 1 ( substitute d = 4 )

3 | - 4 + 2 | + 1

= 3 | - 2 | + 1

= 3 × 2 + 1

= 6 + 1

= 7

HELP ME PLEASE I AM DESPERATE THIS IS ALMOST DUE!!!!!
What is the slope for this graph?

Answers

Answer: The answer is 2

Step-by-step explanation:

Please mark me as Brainiest

Answer: The answer is 2

Step-by-step explanation:

NEED ASAP IT WAS DUE LAST WEEK
1.Explain why the equation (x-4)^2-28=8 has two solutions. Then solve the equation to find the solutions. Show your work.

Answers

(x-4)^2-28=8
Sorry if it’s hard to see

Find the cube of the number 50​

Answers

Answer:

125000

Step-by-step explanation:

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