Consider (cosine (StartFraction pi Over 2 EndFraction) = I sine (StartFraction pi Over 2 EndFraction) ) and z = 3 (cosine (StartFraction 3 pi Over 2 EndFraction) = I sine (StartFraction 3 pi Over 2 EndFraction) ).. What is w + z expressed in polar form?
Answers
The sum of given complex numbers in polar form as [tex]w+z=cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} )[/tex]
What is complex number?"The number of the type a + ib is called as complex number, where a, b are real numbers and [tex]i=\sqrt{-1}[/tex] "
What is polar form of the complex number?"The polar form of a complex number z = x + iy is [tex]z=r(cos\theta+i~sin\theta)[/tex] where [tex]r=\sqrt{x^2+y^2}[/tex] and [tex]\theta=tan^{-1}({\frac{y}{x} })[/tex] "
For given question,
We have been given two complex numbers in polar form.
[tex]w=4(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))~,z=3(cos(\frac{3\pi}{2} )+i~sin(\frac{3\pi}{2} ))[/tex]
The sum of given complex numbers would be,
[tex]w+z= 4(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))+3(cos(\frac{3\pi}{2} )+i~sin(\frac{3\pi}{2} ))[/tex]
We know that
[tex]cos(\frac{\pi}{2} )=0\\\\sin(\frac{\pi}{2} )=1\\\\cos(\frac{3\pi}{2} )=0\\\\sin(\frac{\pi}{2} )=-1[/tex]
So, the sum of given complex numbers would be,
[tex]w+z\\\\= 4(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))+3(cos(\frac{3\pi}{2} )+i~sin(\frac{3\pi}{2} ))\\\\=4(0+i(1))+3(0+i(-1))\\\\=4(i)+3(-i)\\\\=i\\\\=0+i[/tex]
We can write above sum of complex numbers in polar form as,
[tex]0+i=cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} )[/tex]
Therefore, the sum of given complex numbers in polar form as [tex]w+z=cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} )[/tex]
Learn more about complex numbers here:
https://brainly.com/question/5530181
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Answer:
b on edge
Step-by-step explanation:
Related Questions
Eighteen more than five times a number is 153. What is the number?
Answers
Answer:
[tex]\huge\boxed{\texttt{The number is 27.}}[/tex]
Step-by-step explanation:
In order to find the number we need to set up an equation where we represent the unknown number as a variable. I'll call it [tex]n[/tex].
5 times a number can be represented as [tex]5n[/tex].
18 more than that can be represented as [tex]5n+18[/tex].
We know it equals 153, so [tex]5n+18=153[/tex].
We can solve for n by reversing the equation until we have n isolated on one side.
Subtract 18 from both sides:
[tex]5n=135[/tex]
Divide both sides by 5:
[tex]n = 27[/tex]
So our unknown number is 27.
Hope this helped!
x/6= -3
what is x
thank you!
Answers
Answer:
x/6=-3
to undo division between x and 6, multiply both sides by 6
(6)x/6=-3(6)
x=-18
How to write 11 plus the product of 4 and 6 then divide by 5.
Answers
Answer:
(11+(4*6))/5
✌
Answer:
11+(4*6)/5
Step-by-step explanation:
*= multiplication
/= division
Plz name me brainliest I would greatly appreciate it Thank You
Leonardo and Asha are solving the equation (256−247)(4x−19)=5x+14 separately. The results of their first steps are shown below. Leonardo: 256(4x−19)−247(4x−19)=5x+14 Asha: 9(4x−19)=5x+14 Which student has taken the better first step, and why? A. Leonardo, because he has removed the parentheses by using the distributive law B. Asha, because she has simplified the numbers involved in the equation C. Leonardo, because Asha has incorrectly performed subtraction before multiplication D. Asha, because Leonardo has incorrectly applied the associative law
Answers
Answer: B.Asha, because she has simplified the numbers involved in the equation
Step-by-step explanation:
984759.995148 to the nearest whole number.
Answers
Answer:
984760
Step-by-step explanation:
Is this congruent by SSS, SAS, AAS, ASA? Hurry please ASAP! Only if you know!
Answers
Answer:
Side-Side-Side (SSS)
Step-by-step explanation:
I believe these triangles are congruent by the postulate SSS because both triangles have all three sides equal.
Help me or give me answer key plz asap
Answers
Hello, this should help you out!
In this graph, the y values move up 3 units each. Therefore, the blue parabola underwent a translation of 3 units upward.
For further explanation, we see that (0,0) goes up to (0,3), meaning the graph shifted upwards 3 units. So, each y value is raised by positive 3 units!
I hope I was of assistance! #SpreadTheLove! <3
PLEASE HELP ME I WILL VOTE BRAINLIEST
Answers
Answer: 60%.........................
whats wrong with PLEASE PLACE PLASTIC AND GLASS CONTAINERS IN SEPERATE BINS
Answers
Answer:
PLEASE PLACE PLASTIC AND GLASS CONTAINERS IN SEPARATE BINS
The price of a DVD player is $7500.If a sales tax of 8% is charged,find the price at which the DVD player is sold
Answers
Answer:
It will be sold at $8,100.00
Step-by-step explanation:
Frist, you will have to find 8% of 7500, which is $600. Then, taxes are normally added to the original price, so $7500 + $600. This will give you the answer above.
In the following diagram it is know that AC≅BC, DE⊥AD, and m∠C=106°. Using this information find m∠E.
Answers
Answer:
Angle E is 53 degrees.
Step-by-step explanation:
Let's start with the ABC triangle first.
Since AC=BC, angle A and angle B are equal.
We know that the interior angles of a triangle add up to 180.
106 + A + B = 180
A + B = 74
A = B = 37
Moving on to the BDE triangle.
We have angle B = 37 (it's an opposite angle).
We know that angle D is 90, since this is a right triangle.
90 + 37 + E = 180
E = 53
Tien bought movie tickets for herself and two of her friends. She paid $8.50 for each ticket. If Tien has $14.50 left, how much money did she have before she bought the movie tickets
Answers
Answer:
$23
Step-by-step explanation:
add:
14.50
+ 8.50
-------------
23.00
hope this helped!
Anna is 4.5 years older than Kyle. Three times Anna's age, added to six times
Kyle's age is 36. How old are Anna and Kyle
Answers
Answer:
anna is 40.5 yars
Step-by-step explanation:
meeeeeeeeeeeeeeee
Answer:
Step-by-step explanation:
:( :(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(:(
Plsss Help Urgent!!! Which point represents the person who practiced the most and got the fastest time in a swim meet?
Answers
Answer:
Point X
Step-by-step explanation:
Husky Shipping Company charges a flat rate of $150 plus $0.60 per pound to transport freight in the metro area. This cost is represented by the function below where w is the weight of the freight in pounds and c(w) is the cost given the weight of the freight. How much does Ferdinand Freight Company charge to transport freight weighing 1,500 pounds?
Answers
Answer:
Total cost = $1,050
Total cost = Fixed charges + Variable charges[Total weight]
Step-by-step explanation:
Given:
Fixed charges = $150
Variable charges = $0.60
Total weight = 1,500 pound
Find:
Total cost
Computation:
Total cost = Fixed charges + Variable charges[Total weight]
Total cost = 150 + 0.60[1,500]
Total cost = 150 + 900
Total cost = $1,050
please help? 20 points!!!!!!!!!!!!!!!!!!
Answers
Answer:
Year 12
They will be 62 inches
Brainliest plz took me so loong
Step-by-step explanation:
Year 1: Eva 40, Naomi 29
Year 2: Eva 42, Naomi 32
Year 3: Eva 44, Naomi 35
Year 4: Eva 46, Naomi 38
Year 5: Eva 48, Naomi 41
Year 6: Eva 50, Naomi 44
Year 7: Eva 52, Naomi 47
Year 8: Eva 54, Naomi 50
Year 9: Eva 56, Naomi 53
Year 10: Eva 58, Naomi 56
Year 11: Eva 60, Naomi 59
Year 12: Eva 62, Naomi 62
Equation:
12 years so
Eva's equation: 12x2=24 24+38=62
Naomi's equation:12x3=36 36+26=62
After 3 months of living at her new apartment, Renae had 1 dog. Eight months later, Renae still had 1 dog. Which of the graphs below models Renae's dog population?
Answers
Answer:
The graph would need to go through the coordinates (0, 1) and (8, 1) instead of (1, 0) and (1, 8); we would plot the population on the y (dependent) axis and time on the x (independent) axis.
Jaime's scores on tests are: 70, 98, 94, ___ , ___ . What is the lowest score she can get on the fourth test an still have a chance for a 90% test average ? (Assume grades are from 0 to 100)
Answers
Answer:
Step-by-step explanation:
90*4 tests would be 360
360-70-98-94=98
Jamie will need at least a 98 to keep an average of 90%
i need help with this question theres a picture below
Answers
Answer:
Communative Property
Step-by-step explanation:
Communative property states a+b=b+a
. HELP DUE IN A FEW MIN ASAP im stupidssssss
Find the area of a rectangle with length of 80 inches and width of 17 inches.
A) 340 square inches
B) 1360 square inches
C) 680 square inches
D) 1020 square inches
Answers
Answer:
B
Step-by-step explanation:
80*17=1360/choice B
THIS IS MATH
DO ALL QUESTIONS PLEASE AND ILL GIVE BRAINLIEST!!!
Answers
Answer:
ok
Step-by-step explanation:
Answer:
27
Step-by-step explanation:
To solve this problem, let us follow it step by step;
Let Peter's number = P;
So;
⇒ P - 17
⇒ -2 (P - 17 )
⇒ -2 (P - 17 ) = -20
Solve the problem for P;
-2 (P - 17 ) = -20
-2P + 34 = -20
-2P = -20 -34
-2P = -54
P = 27
Step-by-step explanation:
HELP! i’ll mark you as brainliest
Answers
Answer:
m<F = 79 degrees
Step-by-step explanation:
As per the given information;
m<E = 22, the triangle EDF (the one that is given in the picture) is isosceles (meaning that the sides are congruent).
In an isosceles triangle, (a triangle where the sides are congruent) the base angles (the angles opposite to the two congruent sides) are also congruent. One should also know, that in an isosceles triangle, like in any triangle, the sum of the measures of the angles equals 180 degrees.
Using this we can say that
m<D = m<F
To keep it simple while solving the problem, let's say that they have a value of x degrees.
So,
m<E + m<D + m<F =180
Subsitute
22 + x + x = 180
Simplify and inverse operations
22 + x + x = 180
-22 -22
2x = 158
/2 /2
x = 79
So the measure of <D and <F is 79 degrees.
Answer:
79
Step-by-step explanation:
An acute triangle adds up to 180
subtract 22 from 180
180-22 = 158
divide by 2
158/2 = 79
HELP NEEDED ASAP I WILL GIVE BRAINLIEST I'M DESPERATE
Answers
Sorry I don't know how to answer number 3
This is for number 4
x < 3
Explanation:
5 x − 2 x < 7 − 1
3 x < 6
x < 2
Answer:
3. x = 4
4. undefined (anything divided by 0 is undefined)
Step-by-step explanation:
3. You can do anything here:
2(4x - 5) + 3 = 5x + 5
Expand
8x - 10 + 3 = 5x + 5
8x - 5x = 5 + 10 - 3
3x = 12
x = 4
4. 5x - 7 = 2x + 1 + 3x
5x - 2x - 3x = 1 + 7
0x = 8
undefined (anything divided by 0 is undefined)
Please help lol can't figure it out help
Answers
Answer: A- 3 3/10 feet
Step-by-step explanation:
Multiply 5 and 1/2 by 3/5 to get 3 and 3/10 feet. I prefer decimals so you could use 5.5 x 0.6 and get 3.3. It's the same thing but if it's in fractions you should multiply by using fractions.
Drag a graph to each category based on the slope of the graph. IM GIVING YOU 26 POINTS HERE PEOPLE!!!!
Answers
Answer:
The first picture goes with the second sentence.
The second picture goes with the first sentence.
The third picture goes with the third sentence.
The fourth picture goes with the fourth sentence.
Step-by-step explanation:
Pythagorean Theorem Coloring By Number
Plis help , I don’t understand this assignment!!!!
Answers
Answer:
Ahh. I see your troubles with this.
Step-by-step explanation:
So what the paper wants you to do is utilize the Pythagorean Theorem, to find the answer to each question, and whatever answer that turns out to be, you'll color the square with that color.
I'll walk you through the first one! I hope you can do the rest on your own.
Okay, the hypotenuse is 10, and one of the legs is 6. Time to input that!
([tex]a^2=b^2+c^2[/tex] <- Pythagorean Theorem, where a is the hypotenuse, b and c are the legs.)
[tex]100=36+x^2\\x^2=64\\x=8[/tex]
There you go, there's your first answer!
This means that you have to color the square Orange!
Happy Pythagoring!
The diagram shows a circle and an equilateral triangle. One side of the equilateral triangle is a diameter of the circle. The circle has a circumference of 48cm. Work out the area of the triangle.
Answers
Answer:
[tex] Area = 101.4 cm^2 [/tex] (3 S.F)
Step-by-step explanation:
Diameter of circle (D) = one side of the equilateral ∆
Circumference of the circle = πD = 48 cm
Thus:
πD = 48
Divide both sides by π
D = [tex] \frac{48}{\pi} [/tex] = 15.3 cm (approximated to nearest tenth)
Since all sides an equilateral ∆ are equal, therefore, and the diameter, D, of the circle given is the same as the length of one side of the ∆, therefore, all sides of the equilateral triangle would be 15.3 cm.
Recall that the area of a triangle can be found if we know lengths of the two sides of the ∆ and the measure of the included angle between both sides.
Since an equilateral ∆ has equal angles, each measuring 60°, then we already have all the information needed to calculate the area of the ∆.
Thus:
Length of the two sides = 15.3 cm and
15.3 cm
Included angle = 60°
Use the following formula:
[tex] Area = \frac{1}{2}ab \times Sin(C) [/tex]
Where,
a = 15.3 cm
b = 15.3 cm
C = 60°
Plug the values into the formula to find the area.
[tex] Area = \frac{1}{2} \times 15.3 \times 15.3 \times Sin(60) [/tex]
[tex] Area = \frac{1 \times 15.3 \times 15.3 \times Sin(60)}{2} [/tex]
[tex] Area = 101.4 cm^2 [/tex] (3 S.F)
AMONG US ANYONE? CODE : DATDKF
Answers
Answer:
GABBY!
Step-by-step explanation:
Even though the discord app blocked you, u can open in browser. just search the login on google, and sign in. Kylon has discord btw
he was last spotted a few minutes ago here: https://brainly.com/question/19353252
Answer:
all good among us lobbies start with a D
Step-by-step explanation:
for deez
Solve:
(1 1/3) 24 = 32
b: 875 + 61/2=
1/2x + 31/2y=
91/5x +91/5=
Please help me
Answers
Answer:
875 + 61/2= 1811/2
1/2x + 31/2y= y + 31x/2xy
91/5x +91/5= 91 + 91x/5
Step-by-step explanation:
I did not understood the question but I hope thet was the Answer
Which type of rock results from melting and cooling of magma?
Answers
Answer:
Igneous Rocks
Step-by-step explanation:
Alsooo this is Mathematics not science