The product of z₁ = 3 · (cos 14π/15 + i · sin 14π/15) and z₂ = 3 √3 · (cos 11π/15 + i · sin 11π/15) in rectangular form with fully simplified expressions is z₁ · z₂ = 7.794 - i · 13.5.
How to determine the product of two complex numbers
Let be two numbers of the form z = a + i · b, where i = √-1, the product of two of these numbers in rectangular form is described by the following formula:
z₁ · z₂ = (a + i · b) · (c + i · d) = (a · c - b · d) + i · (a · d + b · c) (1)
If we know that a = 3 · cos 14π/15, b = 3 · sin 14π/15, c = 3√3 · cos 11π/15, d = 3√3 · sin 11π/15, then the result in rectangular form is:
z₁ · z₂ = 7.794 - i · 13.5
The product of z₁ = 3 · (cos 14π/15 + i · sin 14π/15) and z₂ = 3 √3 · (cos 11π/15 + i · sin 11π/15) in rectangular form with fully simplified expressions is z₁ · z₂ = 7.794 - i · 13.5. [tex]\blacksquare[/tex]
Remark
The statement presents typing mistakes and is poorly formatted, the correct form is introduced below:
Given the complex number z₁ = 3 · (cos 14π/15 + i · sin 14π/15) and z₂ = 3 √3 · (cos 11π/15 + i · sin 11π/15), express the result of z₁ · z₂ in rectangular form with fully simplified fractions and radicals.
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Choose the ratio that is equivalent to this one: 4/7
Answer:
4:7
Step-by-step explanation:
4:7 is the same as 4/7
15<96–q
what is the value of q
Answer: q < 81
Step-by-step explanation:
isolate q
15 < 96 - q
-81 < -q
divide by negative 1 but flip inequality because you are dividing by a negative
81 > q so
q < 81
|-108| divided by |36|+|17|
absolute value of 19/24
Answer:
-19/-24 ?
Step-by-step explanation:
The absolute value is the distance between a number and zero. The distance between −19 and 0 is 19 .
-24 has an absolute value of 24
Answer:
0.791666667 I hope this helped
Step-by-step explanation:
A window has the shape of a rectangle with a semicircle at the top.
Find the approximate area of the window using the dimensions shown.
Answer:
8+pi/2
Step-by-step explanation:
The area of the rectangle on the bottom is 8, or 2*4. The area of the top is half (because it's a semi circle) of pi*r^2, or just 1/2 pi
PLS HELPP- I NEED AN ANSWER ASAP BRAINLY WILL BE GIVEN~
What is the equation
of the line that passes through the point (-2, -3) and has a
slope of -1?
Answer:
Step-by-step explanation:
Hello:
an equation for the line is : y =mx +b (m: is a slope )
given : m = -1
the equation is : y = -x+b
through the point (-2,-3) :-3 =-(-2)+b....... b=-5
the equation is : y = -x-5
Bob is throwing a party. He has 222222 pints of soda. At the end of the party, there are 888 pints of soda.
How many cups of soda were drank during the party?
The number of the pints of soda were drank during the party will be 14 pints.
What is subtraction?It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.
Bob is throwing a party. He has 22 pints of soda.
At the end of the party, there are 8 pints of soda.
Then the number of the pints of soda were drank during the party will be
⇒ 22 – 8
⇒ 14
The number of the pints of soda were drank during the party will be 14 pints.
More about the subtraction link is given below.
https://brainly.com/question/4319655
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Simplify the polynomial then evaluate for x=-1 3x^2-4+2x-1+x^2
Answer:
-3
Step-by-step explanation:
Simplified polynomial: 4x^2 + 2x - 5
Plug in -1: 4(-1)^2 + 2(-1) - 5
= -3
20 characters just for you brainly
Answer:
first and last option
Step-by-step explanation:
the first and the last are increasing from left to right since the slope is positive.
Simplify the expression by
combining like terms:
-3a + 1 + a +5
Enter the number that belongs in the green box.
[? ]a +[ ]
Enter
-2a+6
Solution:Let's simplify this expression by combining like terms.The like terms are-3a, a1, 5Combine them:-3a+a+1+5-2a+6Hope it helps.
Do comment if you have any query.
Use the product-to-sum formula to convert the expression to a sum or difference. Simplify where is possible.
Answer:
sin3t*cos(s)*cos(t)+sin3t*sin(s)*sin(t).
Step-by-step explanation:
sin3t*cos(s-t);
1) cos(s-t)=cos(s)cost+sin(s)sint; then
2) sin3t*cos(s-t)=sin3t*cos(s)*cos(t)+sin3t*sin(s)*sin(t).
PLEASE HELP PLEASE PLEASE HELP
Reason:
Choices A through C all result in 8/3 = 2.667 approximately
In contrast, choice D becomes 2/3 + 4/3 = (2+4)/3 = 6/3 = 2; showing that choice D is not equivalent to choices A through C.
. Carlee surveyed customers as they left a convenience store. She asked them, “How many items did you
purchase?” The results are shown in the line plot.
(a) How many customers were surveyed?
(b) What was the greatest number of items purchased by a customer?
(c) How many customers purchased 9 items?
(d) How many customers purchased at least 5 items?
(e) What was the median number of items purchased?
Answer:
We need the picture of the line plot in order to answer the question
Step-by-step explanation:
I need this answer fast please factorise the following 16gh2 – 8hi + 24h =
Answer: 8h(2gh - i + 3)
Step-by-step explanation:
factorise 8 out as 8 is a comon factor of 16, 8 and 24
factorise h out together with 8 because all of them have h
PLEASE HELP!!!! ILL MARK BRAINLIEST WITH 10O POINTS!!!!!!! WITH EXLANATION!!
Use the diagram below to create a paragraph proof for the statement: "The sine and cosine of complementary angles are equal"
Answer:
Complemenraty angles are two angles with sum of 90°. In the given triangle ∠A and ∠B are complementary.
Now, the sine and cosine
sine = opposite side/hypotenusecosine = adjacent side/hypotenuseFind the sine of ∠A and cosine of ∠B
sin A = BC/ABcos B = BC/ABSince right sides are equal, left sides are equal too
sin A = cos BSimilarly, we can show that
sin B = cos AProved
Help picture below problem 9
Answer:
i think the answer might be E.
the answer is A option that is Angle M
The value of the expression in standard nation is ….. of( 0.00032)(5.2 times 10^6) divided by 6.4 times 10^5
Answer:
The answer is 0.0026
Step-by-step explanation:
0.00032 x 5200000 = 1664
1664 divided by 640000 is 0.0026
Find the distance between the two points in simplest radical form.
(-8,3) and (-2,-5)
Here we would be using distance formula to calculate the distance between those two points.
Points are,
(-8,3) (-2,5)★ Distance Formula :
[tex]\huge \large \boxed{\sf{{d \: = \: \sqrt{(x _{2} - x _{1}) {}^{2} \: + \: (y _{2} - y _{1}) {}^{2} }}}} \: \red\bigstar[/tex]We have :
x1 = -8 x2 = -2 y1 = 3 y2 = -5Substituting the values in the formula :
Refer the attachment.The distance between the pair of points (-8,3) and (-2,-5) in radical form is √100.
What is the distance between the pair of points?The distance formula can be expressed as:
[tex]d = \sqrt{( x_2 - x_ 1 )^2 + ( y_2 - y_1 )^2}[/tex]
Given the coordinates of the pair of points:
Point 1( -8,3 )
x₁ = -8
y₁ = 3
Point 2( -2,-5 )
x₂ = -2
y₂ = -5
Plug the coordinates into the distance formula and simplify.
[tex]d = \sqrt{( x_2 - x_ 1 )^2 + ( y_2 - y_1 )^2}\\\\d = \sqrt{( -2 - (-8) )^2 + ( -5 - 3 )^2}\\\\d = \sqrt{( -2 + 8 )^2 + ( -5 - 3 )^2}\\\\d = \sqrt{( 6 )^2 + ( -8 )^2}\\\\d = \sqrt{36 + 64}\\\\d = \sqrt{100}[/tex]
Therefore, the distance is √100 units.
Learn more about the distance formula here: brainly.com/question/24509115
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solve for x
plss help
Answer:
2
Step-by-step explanation:
These two are similar triangles. 3 corresponds to 9, and x corresponds to 6. Since 3 is being multiplied by 3 to get 9, x*3 should equal 6. Therefore, x is 2.
What is the value of the expression "two less than six times the difference of a number and five" when n = 9?
O22
O 16
O 32
O 31
Given that Cos0=5/13,find a)Tan0,b)Sin0,c)Sec0,d)Co sec0,e)Cot0,
Step-by-step explanation:
cos 0=5/13. B/H
p=√h2 - b2
= √13 square -5 square
=√169 -25
=√144
=12 Ans
Tan0=p/b =12/5. , sin0=p/h =12/13,. sec0= h/b =13/5 ,. Co sec0 =h/p =13/12 , cot0 =b/p=5/12
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Help with all questions in pictures please
Just put the answers please (ex: 1A 2C 3B. etc)
For question number 7 where it says (Which of the following images represents the polar graph of r = 4cos 2θ?) only two of the graphs are shown please if you can include a graph of the correct answer *70Points*
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
Convert point Q to polar coordinates (accounting for correct direction):
[tex]\displaystyle r=\sqrt{x^2+y^2}=\sqrt{(-5)^2+(-5\sqrt{3})^2}=\sqrt{25+75}=\sqrt{100}=10\\\\\theta=\tan^{-1}\biggr(\frac{-5\sqrt{3}}{-5}\biggr)=\tan^{-1}\bigr(\sqrt{3}\bigr)=\frac{4\pi}{3}[/tex]
Thus, the answer is [tex]\displaystyle \biggr(10,\frac{4\pi}{3}\biggr)[/tex], or A
Problem 2
Make polar substitutions:
[tex]x^2+y^2-2x+8y=0\\\\r^2-2r\cos\theta+8r\sin\theta=0\\\\r^2=2r\cos\theta-8r\sin\theta\\\\r=2\cos\theta-8\sin\theta\\\\r=-8\sin\theta+2\cos\theta[/tex]
Hence, the answer is C
Problem 3
Eliminate the parameter:
[tex]x=t+3\\x-3=t\\\\y=t^2+2t\\y=(x-3)^2+2(x-3)\\y=x^2-6x+9+2x-6\\y=x^2-4x+3[/tex]
Hence, the answer is C
Problem 4
Identify [tex]z_1[/tex] and [tex]z_2[/tex] and add the complex numbers:
[tex]z_1+z_2=(-3+5i)+(-5-2i)=-3+5i-5-2i=-8+3i[/tex]
Thus, the correct answer is S
Problem 5
Use the formula for multiplying complex numbers in polar form:
[tex]z_1z_2=r_1r_2(\cos(\theta_1+\theta_2)+i\sin(\theta_1+\theta_2))\\z_1z_2=(5)(15)(\cos(240^\circ+135^\circ)+i\sin(240^\circ+135^\circ))\\z_1z_2=75(\cos375^\circ+i\sin375^\circ)\\z_1z_2=75(\cos15^\circ+i\sin15^\circ)[/tex]
Hence, the answer is A
Problem 6
Determine when the ball first hits the ground:
[tex]y=-\frac{1}{2}gt^2+(v\sin\theta)t+y_0\\0=-\frac{1}{2}(32)t^2+(58\sin19^\circ)t+1.9\\0=-16t^2+(58\sin19^\circ)t+1.9\\t\approx1.273[/tex]
Determine the horizontal distance covered by the ball:
[tex]x=(v\cos\theta)t\\x=(58\cos19^\circ)(1.273)\\x\approx69.811[/tex]
Hence, the best answer is C
Problem 7
The equation is in the form of [tex]r=a\cos(n\theta)[/tex] where [tex]a[/tex] is the length of each petal and the curve has a horizontal pole. If [tex]n[/tex] is odd, then there are [tex]n[/tex] petals, but if [tex]n[/tex] is even, then there are [tex]2n[/tex] petals.
From our given equation, there are clearly 4 petals since [tex]n[/tex] is even, and each petal length is 4 units. Hence, the first graph is correct.
Fill in the table using this function rule. (Fill Y side)
Y=10x+3
X Y
-1
0
1
5
Answer:
[tex]y = -7[/tex]
[tex]y = 3[/tex]
[tex]y = 13[/tex]
[tex]y = 53[/tex]
you bought 4 jumbo cookies for $5. whats the cost per cookie?
Answer:
80 Cents for each jumbo cookie
In what fraction of their games did Darnel's team score 2 or more runs?
Answer:
0.75 or 3/4Step-by-step explanation:
According to the given box plot, the 25% point matches the number 2.
It means the rest of the scores are 2 or more runs:
100% - 25% = 75% = 0.75 = 3/4 of all the runs
The first term of an A.P is 3 and the fifth term is 9.Find the number of terms in the progression if the sum of the progression is 81.
Answer:
its A becauss i tryed b and th en i tried A so its a
A bag of balloons contains 4 red balloons, 11 green balloons, 15 yellow balloons, and 8 orange balloons. What is the probability that
a randomly selected balloon would be green or orange?
A. 23/38
B. 13/19
C. 15/38
D. 1/2
Answer:
D 1/2
Step-by-step explanation:
Probability is the ratio of the number of favorable outcomes to the total number of outcomes
number of favorable outcomes = 11+8 = 19
total number of outcomes = 38
The probability that a randomly selected balloon would be green or orange is
19/38 = 1/2
The perimeters of two similar right triangles have a ratio of 3 to 5. If the height of the larger triangle is 12 meters, what is the height of the
smaller triangle?
Answer:
7.2 meters
Step-by-step explanation:
Similar triangles have linear dimensions that are proportional. The ratio of heights will be the same as the ratio of permeters:
h/(12 m) = 3/5 . . . . . . . small/large
h = (3/5)(12 m) = 7.2 m . . . . . . multiply by 12 m
The height of the smaller triangle is 7.2 meters.
can some one help me do this question
just give me e and f
Answer:
I believe the answer should be 90:90:180. I may be wrong.
