20 POINTS
Using mathematically precise language, explain in detail how you would multiply the complex number
z1=r1 (cos theta1+isin theta 1)
with the complex number
z2=r2 (cos theta 2+isin theta 2)
r-radius/radii
m-modulus/moduli
theta-argument represent angle theta
The product complex number is z1z2 = r1r2[cos (θ1+θ2) + isin (θ1+θ2)]
[tex]Z_1\times Z_2= r_1(cos \theta_1 + isin \theta_1) \times r_2(cos \theta_2 + isin \theta_2)[/tex]
r-radius/radii
m-modulus/moduli
theta-argument represent angle theta
[tex]= r_1r_2(cos \theta_1 + i sin \theta_1) (cos \theta_2 + isin \theta_2)[/tex]
[tex]= r_1r_2(cos \theta_1 cos \theta_2 + i cos \theta_1 sin \theta_2 + i sin \theta_1 cos \theta_2 + i^2sin\theta_1sin\theta_2[/tex]
What is the value of i square in complex number?The value of i square is
[tex]i^2=-1[/tex]
Therefore,we get,
[tex]= r_1r_2(cos \theta_1 cos \theta_2 + i cos \theta_1 sin \theta_2 + i sin \theta_1 cos \theta_2 + (-1)sin \theta_1 sin \theta_2)[/tex]
[tex]= r_1r_2(cos \theta_1 cos \theta_2 + i cos \theta_1 sin \theta_2 + i sin \theta_1 cos \theta_2 - sin \theta_1 sin \theta_2)[/tex]
Since we know that,
[tex]cos(\theta_1+\theta_2)=cos\theta_1cos\theta_2-sin\theta_1sin\theta_2[/tex]
[tex]sin(\theta_1+\theta_2)=sin\theta_1cos\theta_2+cos\theta_1sin\theta_2[/tex]
So using above value we get,
[tex]= r_1r_2(cos \theta_1 cos \theta_2 - sin \theta_1 sin \theta_2) + i (cos \theta_1 sin \theta_2 + sin \theta_1 cos \theta_2)[/tex]
[tex]=r_1r_2cos(\theta_1+\theta_2)+isin(\theta_1+\theta_2)[/tex]
Therfore the product of the complex number is z1z2 = r1r2[cos (θ1+θ2) + isin (θ1+θ2)].
To learn more about the product of complex number visit:
https://brainly.com/question/1462345
please helppppp i will mark brianlisttt!!!
Answer:
37 degrees
Step-by-step explanation:
A triangle has to be 180 degrees so you do 53+90 (because it is a right triangle) equals 143
then do 180-143 to get your final angle of 37
Answer:
37 degrees
Step-by-step explanation:
The degrees of a triangle will add up to equal 180 degrees. A right angle will always be equal to 90 degrees.
Set up an equation:
Variable x = degrees of the acute angle
90 + 53 + x = 180
143 + x = 180
143 - 143 + x = 180 - 143
0 + x = 37
x = 37
Help please let me know if I’m wrong or right pls!!!!
Answer:
you are correct! nonlinear
Step-by-step explanation:
when this equation is graphed it forms a curved line-- making it non linear :)
Explain the steps on how u got the answer
••••••••••••••••••
Answer:
volume of cyclinder=πr²h
=3.14×2²×3=37.68cm³
rectangular prism volume=6×5×7
=210cm³
total volume=37.68+210=247.68cm³
Step-by-step explanation:
1) Cylinder
d = 4 cm
h = 3 cm
r = d : 2
= 4 : 2
= 2
V. Cylinder = πr²h= 3.14 × 2² × 3
= 37.68 cm³
2) Rectangular prism
l = 6 cm
w = 5 cm
h = 7 cm
V = l . w . h= 6 . 5 . 7
= 210 cm³
3) Total Volume
V. Cylinder + V. Rectangular prism= 37.69 + 210
= 247.68 cm³
#CMIIWI need help pls hurrrryyyyyyyy
Answer: 48
Step-by-step explanation:
30-2 is 28 and 4 times 4 times 5 is 80 and 2 times 2 is 4 and 80 divided by 4 a 20 and 28 plus 29 is 48.
Round to the nearest hundredth (2 decimal places) when necessary
Answer:
if ur asking for area, it is 193.52 ft²
Step-by-step explanation:
16.4 x 11.8
Answer:
193.52 ft is the area
hope this helps
have a good day :)
Step-by-step explanation:
Which number is located at the point Q on the number line?
Answer:
5/8
Step-by-step explanation:
What are the zeros of this function (g)(x)=3x^2-33x-180
Answer:
3x²-33x-180=3(x²-11x-60)=3(x-15)(x+4)
The roots are x-15=0, x=15 and x+4=0, x=-4
What is the volume of the pyramid in the diagram?
25 cm
h = 15 cm
15 cm
20 cm
1,500 cm
2,500 cm
Answer:
this question answer is 1500cm^3
Enlarge the triangle by scale factor 0.5 using (3, 1)
as the centre of enlargement.
Answer:
(1.5, 0.5)
Step-by-step explanation:
Given the coordinate point (x, y, if it is enlarged by a factor of k, hence the resulting coordinate will be (kx, ky)
Given the coordinate (3,1). If enlarged by a factor of 0.5, the resulting coordinate will be (3*0.5, 1 * 0.5) = (1.5, 0.5)
Answer:
USE: (0,2) (0,4) (-1,4)
Step-by-step explanation:
PLEASE USE THESE CO - ORDINATES IN ORDER TO PLOT THE TRIANGLE AND THEN USE THE LINES TO JOIN IT UP
Always proud to help!
The cereal box below is being cut at the edges. Choose the net below that could be created from the box.
Given side a is 41 units, side b is 23 units and the included angle is 70°. Find the area
Answer:
886.13sq. units
Step-by-step explanation:
If the figure is a triangle
Area of the triangle = 1/2 ab sintheta
Given
a = 41 units
b = 23 units
theta = 70°
Area of the triangle = 1/2 * 41 * 23 sin 70
Area of the triangle = 943 sin70
Area of the triangle = 943(0.9397)
Area of the triangle = 886.13
Hence the area of the triangle is 886.13sq. units
willl give brainlyist
Kevin has two bags. Bag 1 weighs 125 pounds and Bag 2 weighs 97 pounds. How many pounds should Kevin add to Bag 2 so that both bags weigh the same?
A. 28
B. 32
C. 36
D. 42
Answer:
A) 28
Step-by-step explanation:
x + 97 = 125
x = 28
A parallelogram has a height of 3 feet and a base of 4 feet. What is the area parallelogram?
pls answer fast
Answer:
Area is always multiplication. 3*4= 12. Area equals 12 feet.
Step-by-step explanation:
There is probably an equation specific to the base (the parallelogram)- use that formula to plug in the numbers to multiply that give you the area.
what is 50% off 4
What percent 20 of 15 is
Answer:
$2 and 75%????
Step-by-step explanation:
I'm not 100% sure but I think thats right
A real-estate agent conducted an experiment to test the
effect of selling a staged home vs. selling an empty
home. To do so, the agent obtained a list of 10
comparable homes just listed for sale that were currently
empty. He randomly assigned 5 of the homes to be
"staged," meaning they were filled with nice furniture and
decorated. The owners of the 5 homes all agreed to
have their homes staged by professional decorators.
The other 5 homes remained empty. The hypothesis is
that empty homes are not as appealing to buyers as
staged homes and therefore, sell for lower prices than
staged homes. The mean selling price of the 5 empty
homes was $150,000 with a standard deviation of
$22,000. The mean selling price of the 5 staged homes
was $175,000 with a standard deviation of 35,000. A
dotplot of each sample shows no strong skewness and
no outliers.
Answer: t-test for a difference in means
Step-by-step explanation:
edg 2021
The name of the appropriate inference procedure is a t-test for a difference in means.
What is a t-test?A t-test can be defined as a type of inferential statistic which is typically used to compare and show a significant difference between the means of two (2) groups that are drawn from a normally distributed data set (population).
This ultimately implies that, the name of the appropriate inference procedure to conduct a hypothesis test in this scenario is a t-test for a difference in means.
Read more on t-test here: https://brainly.com/question/6589776
#SPJ2
At an ice cream shop, there are 3 different flavors of ice cream and 10 different toppings. How many different outcomes are possible?
Answer:
30 or 1/30
Step-by-step explanation:
The smith family is shopping for a new car
Answer:
Sample response: The Smith family has 2 choices to make, color and style. By the fundamental counting principle, the product of the number of choices of color and style must equal 8. So, there could be 1 color and 8 style choices, 2 colors and 4 styles, 4 colors and 2 styles, or 8 colors and 1 style.
Step-by-step explanation:
he red figure is similar to the blue figure. Which choice describes a sequence of transformations in which the blue figure is the image of the red figure?
Dilate the triangle with respect to the origin using a scale factor of 12 and then translate it 4.5 units down and 5 units right.
Dilate the triangle with respect to the origin using a scale factor of 2 and then translate it 6 units down and 8 units right.
Dilate the triangle with respect to the origin using a scale factor of 12 and then translate it 6 units up and 8.5 units left.
Dilate the triangle with respect to the origin using a scale factor of 2 and then translate it 9 units up and 9 units left.
Answer:
Step-by-step explanation:
dilate the triangle with respect to the origin using a scale factor of 2 and then translate it 6 units down and 8 units right.
243.6 ÷ ________ = 02.436
Answer:
...........100.........
Step-by-step explanation:
243.6 ÷100=2.436 we don't use 0 before positive number
Helen bought 1 pint of fruit juice. What is the quantity of fruit juice bought by her in fluid ounces?
A. 10 fl. oz.
B. 12 fl. oz.
C. 16 fl. oz.
D. 20 fl. oz.
Answer:
C. 16 fl. oz.
Step-by-step explanation:
hope this helps.
The figure shown is created by joining three rectangles. Enter the area of the figure, in square centimeters. Round to the nearest hundredth.
Answer:
109.75
Step-by-step explanation:
first, separate the floor into 3 different rectangles to calculate the area and then add them together.
area of rec=L*B
rec 1: 8.5*6=51
rec 2: (9.5-5)*(13.5-5-6)=11.25
rec 3:5*9.5=47.5
Then:
51+11.25+47.5=109.75
You have 48 in a yellow ribbon and 64 inches of red ribbon you want to cut the ribbon into pieces of equal length with no leftovers what is the greatest length of pieces that you can make?
Answer:
16 inches
Step-by-step explanation:
To determine the answer, you have to find the greatest common factor (GCF) of 48 and 64. This is 16 because 16 x 3 = 48 and 16 x 4 = 64.
Help plz
answer 15 points
Answer:
A
Step-by-step explanation:
-9 must be a bigger number then x and it is a greater then not a greater or equal to sign menaing the circle will be empty and the blue part or x will be to the left of -9
Answer:
A
Step-by-step explanation:
Mai says that the equation 2x+2=x+1 has no solution because the left hand side is double the right hand side. Do you agree with Mai? Explain your reasoning.
Answer:
i do
Step-by-step explanation:
the equation would be no solution if the sides are equal numbers with the same slope and do not intersect. if you plug in a random number such as 7 for x you would get 16 = 8. always making the numbers parrallel
Swel 2.) Mental Math: 20 - 12.45 Your answer
Answer:
7.55
Step-by-step explanation:
Is this a school thing or just for random brainly users?
You drop a ball from a height of 1.5 meters. Each curved path has 74% of the height of the previous path.
a. Write a rule for the sequence using centimeters. The initial height is given by the is term n = 1.
b. What height will the ball be at the top of the sixth path?
1) A(n) = 1.5 • (0.74)^x-1; 0.33cm
2)A(n) = 0.74 • (1.5)^x-1; 5.62cm
3) A(n) = 150•(0.74)^x-1; 33.29cm
4) A(n) = 150 • (74) ^x-1; 332,850,993,600cm
Answer:
[tex](a)\ A(n) = 150 * (0.74)^{n-1[/tex]
[tex](b)\ A(6) = 33.29cm[/tex]
Step-by-step explanation:
Given
[tex]a = 1.5[/tex] --- initial
[tex]b = 74\%[/tex] --- rate
Solving (a): The rule of the sequence
First convert [tex]a = 1.5[/tex] to centimeters
[tex]a = 1.5 * 100[/tex]
[tex]a = 150[/tex]
The equation is then calculated using the following geometric progression formula
[tex]A(n) = ab^{n-1}[/tex]
This gives:
[tex]A(n) = 150 * (74\%)^{n-1}[/tex]
Express percentage as decimal
[tex]A(n) = 150 * (0.74)^{n-1[/tex]
Solving (b): The height on the 6th path
This implies that:
[tex]n = 6[/tex]
So, we have:
[tex]A(6) = 150 * (0.74)^{6-1[/tex]
[tex]A(6) = 150 * (0.74)^5[/tex]
[tex]A(6) = 150 * 0.222[/tex]
[tex]A(6) = 33.3cm[/tex]
The double number line shows that in 2 minutes, Pogo the dog can fetch a frisbee 6 times.
0
Time
{
(minutes)
2
+
+
+
Fetches
0
6
Based on the ratio shown in the double number line, how many times will Pogo fetch the frisbee in 4
minutes?
times
Do 4 problems 0000
Answer: try mat way
Step-by-step explanation:
if one lottery player A wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (1-42) and matching the number on the gold ball (1-34). of one ticket is purchased what is the probability of winning the jackpot?
Answer:
1/7140
Step-by-step explanation:
42x5=210
210x34=7140
Can you please mark me brainliest? I'm trying to become a Virtuoso.
Carol's last credit card statement said that she had an account balance of -$107. Which of the following account balances represents a debt greater than Carol's?
A.
-$60
B.
$60
C.
-$154
D.
$154