Complex mathematical

Complex Mathematical

Answers

Answer 1

A) [tex]$x+y=(1+2 \sqrt{3})+(1-\sqrt{3}) i$[/tex]

B) [tex]$y+z=(\sqrt{3}+1)-(2+\sqrt{3}) i$[/tex]

c) [tex]$y-z=(\sqrt{3}-1)-\sqrt{3} i$[/tex]

are the value of given algebraic expression.

What is Complex Number?

The numbers which can be expressed in the form of [tex]$x+iy[/tex] where, [tex]$x, y$[/tex] are real numbers and 'i' is an imaginary number called "iota".

here [tex]$\mathrm{i}$[/tex] is iota whose value is: [tex]$\mathrm{i}=\sqrt{-1}[/tex]

Given .

[tex]$$\begin{aligned}& x=1+\sqrt{3}+2 i \\& y=\sqrt{3}-(1+\sqrt{3}) i \\& z=1-i\end{aligned}$$[/tex]

upon solving two complex number we solve coefficient of iota together and real number together.

A) to find [tex]$(x+y)$[/tex]

[tex]$$\begin{aligned}& x+y=(1+\sqrt{3}+2 i)+(\sqrt{3}-i-\sqrt{3} i) \\& x+y=(1+2 \sqrt{3})+(2-1-\sqrt{3}) i \\& x+y=(1+2 \sqrt{3})+(1-\sqrt{3}) i\end{aligned}[/tex]

B) [tex]$\mathbf{y}+\mathbf{z}$[/tex]

[tex]$$\begin{aligned}& y+z=(\sqrt{3}-i-\sqrt{3} i)+(1-i) \\& y+z=(\sqrt{3}+1)-(2+\sqrt{3}) i\end{aligned}[/tex]

c) [tex]$\mathbf{y}-\mathbf{z}$[/tex]

[tex]$$\begin{aligned}& y-z=(\sqrt{3}-i-\sqrt{3} i)-(1-i) \\& y-z=(\sqrt{3}-1)-\sqrt{3} i\end{aligned}[/tex]

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Related Questions

A circle of radius 8 cm is cut into 6 parts
of equal size, as shown in the diagram.
Calculate the area of each part, giving
your answer correct to 2 decimal places.

Answers

To find the area of each part of the circle, we first need to find the total area of the circle. The formula for the area of a circle is A = πr^2, where A is the area, r is the radius, and π (pi) is a constant approximately equal to 3.14. Plugging in the given values, we find that the total area of the circle is:

A = π * 8^2 = 3.14 * 64 = 201.12 cm^2

Since the circle is divided into 6 equal parts, the area of each part is equal to the total area of the circle divided by 6:

Area of each part = 201.12 cm^2 / 6 = 33.52 cm^2

Rounded to 2 decimal places, the area of each part is 33.52 cm^2.

Answer:  To calculate the area of each part of the circle, we need to first find the total area of the circle and then divide it by the number of parts.

The formula for the area of a circle is A = πr², where A is the area, r is the radius, and π is approximately equal to 3.14.

In this case, the radius of the circle is 8 cm, so the area of the circle is A = π * 8² = 3.14 * 64 = 200.96 cm².

Since the circle is divided into 6 parts of equal size, the area of each part is equal to the total area of the circle divided by the number of parts. Therefore, the area of each part is 200.96 cm² / 6 = 33.49 cm².

Rounded to 2 decimal places, the area of each part is 33.49 cm² ≈ 33.50 cm².

Step-by-step explanation:

15 trading cards he wants to give to 5 friends. Each friend gets same number of trading cards

Answers

Answer:

Each friend gets 3 cards

Step-by-step explanation:

Divide 15 by 5 since he is splitting 15 cards with 5 friends.

:D

Find each angle measure to the nearest degree
1) Find m.
5
S
R
5.7
T
please help, show work if possible :)

Answers

Answer:

RS=26.49 m;

ST =14.08 m;

m<R =28°

Step-by-step explanation:

The crew on a fishing boat caught four fish that weighed a total of 1,032 pounds. The tarpon weighed twice as much as the amberjack and the white marlin weighed twice as much as the tarpon. The weight of the tuna was 5 times the weight of the amberjack.

Answers

Using equations, the weights of the four fish are as follows:

Amberjack = 86 poundsTarpon = 172 poundsWhite Marlin = 344 poundsTuna = 430 pounds.

What are equations?

Equations are mathematical statements showing the equality of two mathematical expressions.

Using the equation sign (=), equations depict that expressions are equal or equivalent.

The total weight of the four fish = 1,032

Let the weight of the Amberjack = x

Weight of the Tarpon = 2x

Weight of the White Marlin = 4x (2 x 2x)

Weight of the Tuna = 5x

x + 2x + 4x + 5x = 1,032

12x = 1,032

x = 86

Weights:

Amberjack = 86 pounds (x)

Tarpon = 172 pounds (2x)

White Marlin = 344 pounds (4x)

Tuna = 430 pounds (5x)

Total weight = 1,032 pounds (86 + 172 + 344 + 430)

Thus, we solved the weight of each fish using equations.

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Question Completion:

How much did each fish weigh?

The opposite of the opposite of -2 is equal to

Answers

The opposite of the opposite of -2 is equal to: -2

This can be solved by using the concept of inverse.

What is inverse?

This quantity is also referred to as the opposite (number), sign modification, and negation. It changes the sign of a real number so that the additive inverse of a positive number is negative and the additive inverse of a negative number is positive. Due to their ability to reverse mathematical processes, inverse techniques are crucial for solving equations. One of the most crucial issues to ask whenever a new mathematical method is presented is how to invert it.

The term inverse in mathematics refers to the inverse of another operation.

In this case firstly opposite of - 2 is 2 and next opposite of 2 is again -2.

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A netball court measures 31 metres long and 15 metres wide.
What is the perimeter of a netball court?

Answers

The perimeter of the netball court is equal to 92 meters.

What does perimeter mean?

The whole distance encircling a shape is referred to as its perimeter. It is the length of any two-dimensional geometric shape's boundary or outline.

A netball court is a rectangle,

it is given that length of the net ball court is equal to 31 meters.

The width of the netball court is equal to 15 meters.

Therefore the perimeter of the netball court is equal to the length of all sides of the rectangle.

Perimeter of netball court = 2(31+15)=92 meters.

Therefore perimeter of the netball court is equal to 92 meters.

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10 POINTS!
What is the constant of proportionality in this proportional relationship?

x 2 4 6 8
y 5/6 1 2/3 2 1/2 3 1/3

A. 12
B. 5
C. 12/5
D. 5/12

Answers

Answer:

d

Step-by-step explanation:

The constant of proportionality in a proportional relationship is the number that relates the two variables, x and y, in the equation y = kx.We can see that the relationship between x and y is in the form of y = kx. We can find the constant of proportionality (k) by dividing the y-value by the corresponding x-value.For example:

x = 2; y = 5/6

k = y/x = (5/6) / 2 = 5/12The constant of proportionality is 5/12 for the given proportional relationship,

y = kx where k = 5/12Note that it is important to understand that the relationship is a proportion because in this case, the k(constant) is the same for every point, if we calculate each (y/x) point it will be 5/12

3
Use the drawing tool(s) to form the correct answer on the provided graph.
The function f(x) is shown on the provided graph.
Graph the result of the following transformation on f(x).
Drawing Tools
Select
Line
Click on a tool to begin drawing
-10
-8
f(z) + 6
-6
4
-2
10-
8-
6
Delete
Undo
Reset
10 i need help with this

Answers

Start at -2 on the y-axis, count up until it is on a corner of the graph, then move 4 up on the y-axis and once to the right, making the fraction 4/1.

what is transformation ?

Four various modifications that can be made to a point, line, or geometric object are referred to as transformations collectively. You must be able to identify which changes have been made and that each alteration has been made. The following guidelines for function translation and transformation: The function is shifted up by b units by F (x) + b. F (x) b causes the function to move downward. The expression f (x + b) causes the function to be moved left b units. Translation, reflection, rotation, and dilation are the four different types of transformations. Transform, reflect, or rotate the geometric shapes that are displayed on a coordinate plane. The transformation, often known as f: X X, is the name given to a function, f, that maps to itself.

given

-1 on the left x-axis and 4 on the right y-axis

Start at -2 on the y-axis, move up the y-axis six times, and you should arrive at 4. However, you must identify the first line in order to complete the puzzle.

Start at -2 on the y-axis, count up until it is on a corner of the graph, then move 4 up on the y-axis and once to the right, making the fraction 4/1.

Since you should be at 4, apply the formula rise/run 4/1 to ascend 6 on the y-axis.

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Population Growth

Using the graph, find the value of y when x = 7.

a. y = 7 c. y = 2.71
b. y = 6.1 d. y = 4.42

Please select the best answer from choices provided

Answers

Answer:

D. y = 4.42

Step-by-step explanation:

I calculated it logically

Please help me faster if know please?!!!!

Answers

.83

25 bus riding sophomores / 30 sophomores

PLZ HELP NO LINK PPPPLLLLLLLLLZZZZ

Answers

Answer:

its A

Step-by-step explanation:

Answer:

uhk3rbfghsfbhufevhjb

Step-by-step explanation:

give me brainlest

If m∠A = 29°, m∠B = 84°, and c = 14, what are the measures of the remaining sides and angle?

Answers

Answer:

m∠C = 67°, a = 7.37, b = 15.13

Step-by-step explanation:

There are 180° in a triangle. We know two angles in the triangle, so we can calculate the third angle.

Since this is not a right triangle, we will use the Law of Sines.

SinA/a = SinB/b = SinC/c

see image.

What must the values of x and y be so that the two houses are similar?

Answers

your answer on the page is c

Please help, no links

Answers

Each angle is 90°

A rectangle always has equal corners

Solve: 63z2+61z=−6. Multiple answers

Answers

z = -1/9 , -6/7

Have a nice day!

Decide whether triangles ABC and DEC are similar. Explain or show your reasoning.

Answers

Triangles ABC and DEC are similar.

What is triangle?

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

Here, we have,

Given the triangles ABC and DEC

For the triangle ABC:

m∠A = 36, m∠B = 21

So, the m∠C = 180 - (m∠A + m∠B ) = 180 - (36 + 21) = 123

Similarly, the angles of DEC are,

m∠D=36 , m∠C=123 & we get,  m∠E =21

So, comparing the measurements of the angles of both triangles:

m∠A=m∠D.

m∠C=m∠C

m∠B=m∠E

So, the triangles are similar using the AAA postulate.

Hence, triangles ABC and DEC are similar.

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help me plzzzzzzzzz
solve for x

Answers

Answer:

[tex]7) \frac{x+20}{x}=\frac{46}{30}[/tex]

[tex]30(x+20)=46x[/tex]

[tex]30x+600=46x[/tex]

[tex]46x-30x=600[/tex]

[tex]16x=600[/tex]

[tex]x=75/2[/tex]

[tex]x=37.5[/tex]

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

[tex]8) \frac{10}{3x+1} =\frac{22}{7x-1}[/tex]

[tex]10(7x-1)=22(3x+1)[/tex]

[tex]70x-10=66x+22[/tex]

[tex]70x-66x=22+10[/tex]

[tex]4x=32[/tex]

[tex]x=\frac{32}{4}[/tex]

[tex]x=8[/tex]

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

hope it helps...

have a great day!!

Which expression is equal to:
³ × ³ × ³ × ³ × ³ × ³ × ² × ³ ×
3
X
4
3
4

Answers

3 x 3 x 3 x 3 x 3 x 3 x 2 x 3 x 3 x 434 = 5,694,948

Only answer if you’re sure :) need the whole answer! Will give Brainly

Answers

Answer:

Step-by-step explanation:

y = -1x + 1

y = -x + 1

I'm sure  :P

Answer:

y=-1x+1

Step-by-step explanation:

the slope is 1/1 and line is declining hence the negative

Here is a list of numbers:
14, 4, 4, 16, 14, 3, 13 ,11 ,1 ,8
State the median.

Answers

Answer:

the Median is 9.5

no links PLEASE HELP DUE IN 10 MINUTES you can use a calculator if you want. No links please help this is very important i will give you brain thing if its correct

Answers

Answer:

0.334

Step-by-step explanation:

Basically to show reasoning: 16*215= 3340

4 decimal places, so you would move it four decimal places from 3340.

Which equals to: 0.334

Hope this helped! :)

What is the slope of the line that is perpendicular to the line y = -2x + 5?
slope =

Answers

Answer:

The perpendicular line is vertical and the slope is undefined.

Step-by-step explanation:

Slope : - 2
Y intercept : ( 0,5 )

a skier travels 4 seconds and cover 72 meters. how long will it take the skier to travel 360 meters?

Answers

It should take 20 seconds for the skier to travel 360 meters.

Can someone help me out. Paying big points

Answers

Answer:

1) the quadrants go counter clockwise, Quadrant I is the upper right square, Quadrant II is the upper left square, Quadrant III is the lower left square, and Quadrant IV is the lower right square.

2) Quadrant II

3) Quadrant IV

4) Quadrant III

5) Quadrant I

6) Both would be on the horizontal axis

7) Both would be on the vertical axis

Step-by-step explanation:

Hope this helped!

what is the area shaded in the region?

Answers

Answer:

Option C

The Area Of Shaded Region is 50.2 cm²

Step-by-step explanation:

For A given Circle,

For Small (Non-Shaded) Circle:

Diameter (d) = 6 cm

Radius = d ÷ 2 = 6/2 = 3 cm

For Area of Small (Non-Shaded) Circle

Formula:

A = πr²

A = 3.14 × (3)² cm

A = 3.14 × 9 cm

A = 28.26 cm²

For Area of Big (Shaded) Circle:

Diameter (d) = 10 cm

Radius = d ÷ 2 = 10/2 = 5 cm

For Area of Small (Non-Shaded) Circle

Formula:

A = πr²

A = 3.14 × (5)² cm

A = 3.14 × 25 cm

A = 78.5 cm²

For The Area Of Shaded Region

Area of Big Circle - Area of Small Circle

78.5 cm² - 28.26 cm² = 50.24 cm²

Thus, The Area Of Shaded Region is

50.2 cm²

-TheUnknownScientist

Answer:

3rd option

50cm2

Step-by-step explanation:

50cm2

explanation is given above

A, B, C, or D?
and an explanation

Answers

the answer would be d

Answer:

A

Step-by-step explanation:

any help please — Put the fractions 12,38 and 34 in order from smallest to largest. Find the value of 113+256.

Answers

The value of 113+256 is determined by the above fractional formulae. Is 369

Why are fractional equations difficult to solve?

An exact number that shows a percentage of a total is called a fraction. You may figure it out by dividing a sum by the quantity of parts. As an example, the number 12 represents one-half of a whole number or an object. Simple subtraction of the smaller numerator from the larger numerator will yield the solution to the problem. To solve, for instance, 6/8 - 2/8, just take 2 out of the answer. The answer, which can be abbreviated to "4/8," is 12, or 12.

Making a fraction simpler by reducing or simplifying it is our goal. In order to do this, we divide the denominator and numerator by the largest integer that can be divided into both integers precisely. That is to say,

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rectangular cards 2 inches by 3 Inches are cut from a rectangular sheet 2 ft by 3 ft what is the greatest number of cards that can be cut from the sheer?

Answers

Answer:

144

Step-by-step explanation:

3ft = 36 inches         card 2x3 = square  6 inches

2ft = 24 inches

36X24 = 864 square inches

864/6= 144

The greatest number of cards that can be cut from the sheer if rectangular cards 2 inches by 3 Inches are cut from a rectangular sheet 2 ft by 3 ft is 144.

What is Rectangle?

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.

Given:

The dimension of rectangular card = 2 inches × 3 inches,

The dimension of rectangular sheet = 2 ft  × 3 ft,

We know that 1 foot = 12 inches,

The dimension of a rectangular sheet = 24 inches × 36 inches

Area of sheet = 24  ×  36 = 864 inches²,

Area of card = 2  ×  3 = 6  inches²,

The no of card  = Area of sheet / Area of card

The no of card  = 864 / 6 = 144

Therefore, the greatest number of cards that can be cut from the sheer if rectangular cards 2 inches by 3 Inches are cut from a rectangular sheet 2 ft by 3 ft is 144.

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Plz help me!!!!! 3. &4 only!!!

Answers

Answer:

Step-by-step explanation:

3.

Note that

[tex]L_1 : 4x-y=10 \\ L_2: -2x+4y=16[/tex]

aren't parralel lines. So they are intersected in one point.

Answer: Number of solutions is ONE. The system is soluble

4.

Similarly to 3. Number of solutions is ONE. The system is soluble

A walkway forms one diagonal of a square playground. The walkway is 32 m long. How long is each side?

Answers

Answer:30.45751052, or 30.5

Step-by-step explanation:

since you know that the playground is a square, a diagonal would cut the square into 2 45-45-90 triangles, now that you know that information, there is a really easy way to solve the problem, the way i did it was i used the law of sines, which states that side a/sin(angle A)=side b/sin(angle B). so 32/sin(90)=30.7943... substitute that into the equation and you get 30.7943... =side b/sin(angle B). since you know that angle B =45 degrees take the sin of that and multiply it by 30.7943 to get the answer.

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