What are complex integers ?

Answers

Answer 1

Answer:

In mathematics, a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a symbol, called the imaginary unit, that satisfies the equation i² = −1. Because no real number satisfies this equation, i was called an imaginary number by René Descartes.

Step-by-step explanation:

Complex Integer

(or Gaussian integer), a number of the form a + bi, where a and b are integers. An example is 4 – 7i. Geometrically, complex integers are represented by the points of the complex plane that have integral coordinates.

Complex integers were introduced by K. Gauss in 1831 in his investigation of the theory of biquadratic residues. The advances made in such areas of number theory as the theory of higher-degree residues and Fermat’s theorem through the use of complex integers helped clarify the role of complex numbers in mathematics. The further development of the theory of complex integers led to the creation of the theory of algebraic integers.

The arithmetic of complex integers is similar to that of integers. The sum, difference, and product of complex integers are complex integers; in other words, the complex integers form a ring.

Answer 2

Answer:

An immediate consequence of the definition of arithmetical operations on complex numbers is that the sum, the difference, and the product of two or more complex numbers.

Step-by-step explanation:


Related Questions

please give me the correct answer. T^T

Answers

Answer:

All pairs of corresponding sides are congruent

Step-by-step explanation:

∠A≅∠D

∠B≅∠E

∠C≅∠F

Find the measure of X

Answers

Answer:

x = 6

Step-by-step explanation:

When parallel lines are intersected by a transversal

alternate exterior angles are congruent

Therefor

15(x + 2) = 120

Divide both sides by 15

x + 2 = 8

Subtract 2 from both sides

x = 6

Answer:

Step-by-step explanation:

here 120 degrees would be the same as 15(x+2)

Just like how angle R on the other side of 120 Degrees is the same

so 15(x+2) = 120 degrees

let us distribute

15x +30 = 120

      -30     -30

15x=90

15x/15=90 /15

x=6

so what you have selected is correct

find CP when sp=47180 loss=5%​

Answers

Answer:

The cost price 49,359

Step-by-step explanation:

To find the loss, turn 5% to decimal then multiply it to the selling price

5% = 0.05

47,180 * 0.05 = 2,359

The loss is 2,359.

Now add it to the selling price to find the cost price.

47,180 + 2,359 = 49,539

3.) What would 9 gallons of gas cost at $2.12 per gallon? *
$18.80
O $17.56
$19.08
$11.12

Answers

Answer:

19.08

Step-by-step explanation:

each gal = $2.12

gals filled = 9

9 x 2.12 = 19.08

Find the total surface area in square units of the figure below by creating a net.

Answers

So , start if by 5x10 = 50 50x3= 150
That’s the area for our rectangles
Then 8x6=48 this is normally divided in half but since there are 2 triangles it can just remain that way , so 150+48=198 I think I’m correct

Joshua wants to buy a flat-screen TV that costs $625. He saves $62.50 each week to buy the TV. In how many weeks will he have enough money to make his purchase?
A. 8
B. 9
C. 10
D. 11

Answers

Answer:

C. 10 weeks

Step-by-step explanation:

Joshua wants to buy a flat-screen TV that costs $625. He saves $62.50 each week to buy the TV. In how many weeks will he have enough money to make his purchase?

A. 8

B. 9

C. 10

D. 11

cost of television divided by weekly savings = number of weeks

625 : 62.50 = 10 weeks

Can someone help me pls!? Question 5 (Essay Worth 5 points) Determine the answer to (-5) + 4 and explain the steps using a number line​

Answers

Answer:

-5+4= -1

Step-by-step explanation:

On a number line, look at -5, then add 4 to that, aka moving it up 4 places. -1 would be where it ends up.

CHINESE SOCIAL CREDIT POINTS

What do you think about Mao Tse-tung

Answers

Answer:Stuff Step-by-step explanation:

watch out for people who post links as an answer to your questions. they will mess up your account​

Answers

Answer:

OK THX

Step-by-step explanation:

Solve pls brainliest

Answers

Answer:

a)0.085 b)19.6 percent

Step-by-step explanation:

Answer:

a) 0.085

b) 19.6%

Step-by-step explanation:

Weather report, pls help me y’all i don’t wanna fail this class i beg you plss

Answers

Answer:

1

Step-by-step explanation:

3. Consider the product -11 7 6/7.
(a) Determine the product by rewriting the mixed number and applying the distributive property. What is the product?
(b) Multiply the integer and mixed number by multiplying fractions. What is the product?

Answers

Answer:

Did you get the answer to this. I am struggling on this as well.

Step-by-step explanation:

a recipe calls for 24 fluid ounces of light whipping cream. if anthony has 1.5 pints of whipping cream in his refrigerator does he have enough for the recipe

Answers

Answer:

Yes

Step-by-step explanation:

He has 24 fluid ounces. You know this because in 1 pint, there are 16 fluid ounces. In half of one pint there are 8 ounces. 16 + 8 = 24 oz

I hope this could help!

Answer:

yes and he will have 4.8228 fluid ounces left over

Step-by-step explanation:

1.5 pints + 28.8228 US fluid ounces

If
x
=
5
and
y
=
7
, evaluate the following expression:
100

3
(
3
y

4
x
)

Answers

Answer:

97

Step-by-step explanation:

100-3(3y-4x)

97(3×7-4×5)

97(21-20)

97(1)

=97

hurry please im dead meat if i cant do this picture below

Answers

Answer:

4 divided by 1/8

hope it helps

Step-by-step explanation:

Pls Solve

Due today
For a grade

First will be Brainliest!

Answers

What do you mean there is no question?

if f(n) = -6n + 2, find t 5/6

Answers

So you need to add 6n with +2 then 5-7

Mark of Ben in semester 1 examination is 586:600. Convert it into percentage

Answers

Answer:

97.67

Step-by-step explanation:

600 = 100%

586 = x%

[tex]\frac{100}{x} = \frac{600}{586}[/tex]

x = [tex]\frac{586.100}{600}[/tex] = [tex]\frac{586.100}{6.100}[/tex] = [tex]\frac{586}{6}[/tex] = 97.67

angel 1 and angel 2 form a right angle. Writ a conjecture about each value or geometric relationship

Answers

Answer:

it's angle not angel.

Step-by-step explanation:

PLEASE EXPLAIN THE WORK WHEN YOU ANSWER FOR ME PLEASE


solve each equation:

1: |b-6|=1

2:|b+2|=7

Answers

Answer:

Step-by-step explanation:

theres 2 possible solutions for each equation and each one is right

or for dummies, just reverse the +/- inside the l x +/- y l. and make 2 different equations the first with a + and the second with a -

1. lb-6l = 1

b - 6 = 1

b = 7

-----------

b + 6 = 1

b = -5

--------------

2. lb+2l=7

b + 2 = 7

b = 5

--------------

b - 2  = 7

b = 9

---------------

PLZZZZ HELPPPP MEEEEEE​

Answers

Answer:

13

Hope this helps, have a nice day/night! :D

If it helped, please mark as brainliest!

PLEASE HELP!

Using the information below draw a diagram, making sure to label the sides and angles, to help answer the following 2 questions. Don’t forget to label your answer.

∆ABC ≅∆DEF
AC = 15 in., AB = 24 in., m∠A = 34°, m∠C = 124°
What are the values of DE and m∠E?

DE = ______ m∠E = ________

Answers

Answer:

DE = ____24__    m∠E = ____22____

Step-by-step explanation:

I hope this helps

Answer the questions below, no links.

Answers

Answer:

[Graph] See attached

[Question] A, C, & E

Step-by-step explanation:

[Graph] 0.4 -> 2/5

     () It will go through the origin (0, 0) because we have no b, or y-intercept

     () From (0, 0) it will go 2 up and 5 over, 2 up and 5 over, etc etc

     () See attached

[Question]

     () A, C, E

     () It is proportional (one to one as it is a straight line) so A is correct

     () The slope in y = mx + b is m, and our m is 0.4 so it is the slope

     () 3 * 0.4 = 1.2, so E is correct

Please help me!!! It would really help

Answers

Answer:

  D'(25, 0)

Step-by-step explanation:

Dilation by a factor of 5 about the origin multiplies each individual coordinate by 5.

  (x, y) ⇒ (5x, 5y)

  D(5, 0) ⇒ D'(5·5, 5·0) = D'(25, 0)

Which two ratios make a proportion. a) 9÷12 and 15÷20 b) 4/25 and 17/101


PLZ ANSWER QUICK will mark branilyist.

Answers

Answer:

I think the answer would be b

Plzzzzz help meeeee plzzz

Answers

Answer:

1 Meter equals 100 Centimeters, therefore 1 Square meter is equal to 100 centimeters squared. Thus, [tex]1 M^{2}[/tex] is equal to [tex]100^{2}[/tex] when counting in Centimeters square. Now that we have gotten the basics down, Lets convert the other necessary units.

[tex]1 m^{2} = 10,000 cm^{2}[/tex]

[tex]1 mm^{2} = 0.01cm^{2}[/tex]

[tex]1 km^{2} = 1,000,000 m^{2}[/tex]

Now, using that knowledge, we can find the answers to all questions.

1) 0.15 [tex]m^{2}[/tex]

2) 0.086 [tex]m^{2}[/tex]

3) 0.1 [tex]cm^{2}[/tex]

4) 600,000 [tex]cm^{2}[/tex]

5) 0.0001 [tex]km^{2}[/tex]

6) 400 [tex]cm^{2}[/tex]

7) 52,100 [tex]mm^{2}[/tex]

8) 500,000 [tex]m^{2}[/tex]

9) 0.087 [tex]mm^{2}[/tex]

10) 50 [tex]cm^{2}[/tex]

That's all folks!

Andrew owns stock in Hyren Airlines and as a result gets paid dividends worth $539. 70 every year. If Andrew owns 105 shares of Hyren Airlines, how big is the dividend each share yields? a. $3. 60 b. $2. 78 c. $5. 67 d. $5. 14.

Answers

Answer:

the answer to your question is B $3.60

!!!!!!!!!!!!!!!!!!!!!!!!!#

Answers

[tex]\large\red{┈──┈──┈──┈──┈──┈──┈──┈──┈─}[/tex]

The best option is letter C. t = 2h + 32

C. t = 2h + 32

How do you solve for x

3x^2 = -24x

Answers

[tex]3x^2 = -24x \\\\\implies 3x^2 +24x =0\\\\\implies x^2 +8x = 0\\\\\implies x(x+8) =0\\\\\implies x =0~~ \text{or}~~ x = -8[/tex]

Step-by-step explanation:

3x² = -24x

Divide through by x

3x = -24

x = -24/3

x = -8

Evaluate the expression-3 x + 4 when x = 2.

Answers

Answer:

-2

Step-by-step explanation:

-3x + 4

-3(2) + 4

-6 + 4

-2

Substitute in 2 for x, and solve.

-2 (hope this helps)
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