i si
what is w- z expressed in polar form?
Given wuv5c() + (.) and : ==(--(?) + ()
=(cos1 - +(cosin
o vz(cos() + i sin (4)
o v7(com () + ()
ovi (95) + ()
o r2(com () + i sin (7)
COS
i sin
ST
COS
+ i sin
77
o
+
Answers
Answer:
[tex]w-z=\sqrt{2}\biggr(cos(\frac{3\pi}{4})+isin(\frac{3\pi}{4})\biggr)[/tex]
Step-by-step explanation:
Convert from polar to rectangular
[tex]w=\sqrt{2}(cos(\frac{\pi}{4})+isin(\frac{\pi}{4}))\\\\w=\sqrt{2}(\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i)\\ \\w=1+i[/tex]
[tex]z=2(cos(\frac{\pi}{2})+isin(\frac{\pi}{2}))\\ \\z=2(0+i)\\\\z=2i[/tex]
Subtract the complex numbers
[tex]w-z=(1+i)-2i=1+i-2i=1-i[/tex]
Convert from rectangular (x,y) to polar (r,θ)
[tex]r=\sqrt{x^2+y^2}\\r=\sqrt{1^2+(-1)^2}\\r=\sqrt{1+1}\\r=\sqrt{2}\\\\\theta=tan^{-1}(\frac{y}{x})\\ \theta=tan^{-1}(\frac{-1}{1})\\ \theta=tan^{-1}(-1)\\\theta=\frac{3\pi}{4}\\ \\w-z=\sqrt{2}\biggr(cos(\frac{3\pi}{4})+isin(\frac{3\pi}{4})\biggr)[/tex]
Related Questions
Sam buys a bus ticket for $1.60 and a breakfast burrito for $3.75 each day, Monday through Thursday. He leaves a $1.40 tip each day.
Answers
Answer: $22.20
Step-by-step explanation: yw
Solve the system of linear equations by substitution.
y = 2x + 8
y = -2x
Answers
Answer:
(- 2, 4 )
Step-by-step explanation:
y = 2x + 8 → (1)
y = - 2x → (2)
substitute y = 2x + 8 into (2)
2x + 8 = - 2x ( add 2x to both sides )
4x + 8 = 0 ( subtract 8 from both sides )
4x = - 8 ( divide both sides by 4 )
x = - 2
substitute x = - 2 into (2)
y = - 2(- 2) = 4
solution is (- 2, 4 )
Answer: [tex]y=4,\:x=-2[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}y=2x+8\\ y=-2x\end{bmatrix}[/tex]
[tex]\mathrm{Substitute\:}y=-2x[/tex]
[tex]\begin{bmatrix}-2x=2x+8\end{bmatrix}[/tex]
[tex]{Isolate\:}x{for -2x=2x+8[/tex]
[tex]x=-2[/tex]
[tex]\mathrm{For\:}y=-2x[/tex]
[tex]\mathrm{Substitute\:}x=-2[/tex]
[tex]y=-2\left(-2\right)[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]y=4[/tex]
[tex]The\:solutions\:to\:the\:system\:of\:equations\:are:[/tex]
[tex]y=4,\:x=-2[/tex]
Good Luck!
Question within image.
Answers
1)a parallelogram is a quadrilateral with opposite sides being parallel so the lines AB must equal CD or otherwise it wouldn't be a parallelogram
2)for a quadrilateral to be proven to be a parallelogram the consecutive angles has to be supplementary which means they add up to 180 or for example you could slice the parallelogram in half down the middle you could piece the two consecutive angles together to make 180 degrees
10+s=-4 help yall asap this is mad hard
Answers
ANSWER = s = -14
Proof -14+10=s
Evaluate a + b for a = 2 and b = 3.
Answers
Hey there!
a + b
= 2 + 3
= 5
Therefore, your answer is: 5
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Find the value of x.
Answers
Answer:
x = 53
Step-by-step explanation:
The sum of the exterior angles of a convex polygon is always 360°.
x +x +59 +48 +50 +39 +58 = 360
2x +254 = 360 . . . . simplify
x +127 = 180 . . . . . . divide by 2
x = 53 . . . . . . . . . . . subtract 127
you are on a 750 mile trip by car . ur car used seven gallons of gas to travel the first 210 miles of the trip. how much more gas will u need to make it the rest of the way at the same rate ? show work
Answers
Answer:
A total of 18 gallons of more gas
Step-by-step explanation:
7 gallons = 210 miles
750-210= 540
210*2 =420 miles 7*2=14 gallons
210/2= 105 7/2=3.5 gallons
525 miles 17.5 miles
210/14= 15 7/14=.5 gallons
540 miles 18 gallons
There re 380 light bulbs lined up in a row in a long room. Each bulb has its own switch and is currently switched off. Each bulb is numbered and is consecutively from 1 to 380. You first flip every switch. You then flip the switch on every second bulb. You then flip the switch on every third bulb. This continues after you have gone the process 380 times
(I rlly need help)
Answers
Flipping the bulbs is an illustration of sequence and patterns
19 bulbs would remain on.
How to determine the number of bulbs that will be onThe sequence of turning the bulbs off and on, would change the state of the bulbs until the 380th process.
While changing the state of the bulbs, the bulb at the perfect square positions would remain on.
There are 19 perfect square numbers between 1 and 380 (inclusive)
Hence, 19 bulbs would remain on.
Read more about sequence and patterns at:
https://brainly.com/question/26698448
can you simplify 4+6(3)+2(5 1/2 -1)
Answers
Answer:
31
5 1/2 - 1 = 4.5
4+ 18= 22
2(4.5) = 9
22+ 9 = 31
Step-by-step explanation:
How many degrees are there in the angle between the hour and minute hands of a clock is a quarter past two
Answers
The number of degrees there are in the angle between the hour and the minute hands of the described clock is; 30°
Angle measure on a wall clockThe conventional analogue wall clock is numbered 1 to 12.
On this note, there are 12 unit subdivisions on the clock.
Each unit subdivision covers angle measure;
360°/12 = 30°Since, at quarter past two; the hour arm of the clock is on 2 and the minute arm is on 3;
It follows that the degree measure of the angle subtended is; 30°.
Read more on degree measure;
https://brainly.com/question/4221639
A farmer has 696 acres of pasture for sheep grazing, and 40 acres for growing cotton. An average of 8 sheep graze on one acre. How many sheep does the farmer have?
Answers
Step-by-step explanation:
[tex]1 \: acre \: = \: 8 \: sheeps \\ 696 \: acres \: = 8 \times 696 = 5568 \: sheeps[/tex]
There are seven boys and seven girls in a class. The teacher randomly selects one student to answer a question. Later, the teacher randomly selects a different student to answer another question. The first student is a boy and the second student is a girl.
Find the probability
Answers
0.5 for a girl
Seven people are going to share an 84-ounce bottle of soda. How many ounces will each person get to drink?
Answers
Answer:
Each person is gonna drink 12 ounces
Step-by-step explanation:
84 divided by 7 is 12
As it is 7 people sharing one drink that is 84 ounces I divided since they would be sharing equally and as it was the right thing to do.
Not a teacher
Any Suggestions on what to do here? I already restarted my PC twice, cleared my browsing data, and rebooted the wifi network....
Oh yea and whats 5 to the square root of 625
Answers
Answer:
Use a factor tree. For example, 625 = 5 x 125 = 5 x 5 x 25 = 5 x 5 x 5 x 5. Because there are 4 fives, and we are looking for the square root, (5 x 5) (5 x 5) = 625. Therefore the square root of 625 is 25.
Please help me with this! Thank you! Click on the photo for better view!
Answers
Answer:
In order: -5, 3, 5
Step-by-step explanation:
-5g + 15h - 25
-5 ( g - 3h + 5 )
Hopefully this helps!
Brainliest please?
How do you calculate 33% of 500 by first calculating 1% of 500
Answers
Answer:
165
Step-by-step explanation:
first 1% of 500 is calculated and then multiplied by 33:
[tex]\frac{1}{100} (500)=5[/tex]
5(33)=165
Hope this helps
angle A and angle B are supplementary angles. Find m angle A and m angle B.
m angle A=(x+11) m angle B=(x-15)
Answers
2X=176
X=88
angle A 88+11=99
Angle B 88-15= 73
(X+11)+(x-5)=180
X+11+x-15=180
x+x+11=165
2x=165-11
2x=154
— —
2 2
X=77//
Anna is designing the plan of a kitchen using some computer aided design software. the coordinates of the corners of the room on screen are (0,10) (220,10) (0,260) (220,260). she needs to enter the coordinates of the ceiling light, which will be the exactly in the center of the room. what will the coordinates of the light be?
PLEASE HELP ME IF YOU CAN AS SOON AS POSSIBLE. THANK YOU
Answers
(220,10)
Step-by-step explanation:
This reminds me of when I was in middle school
Answer:
(110, 135)
Step-by-step explanation:
From the coordinates given, the shape of the ceiling is a rectangle.
Width = difference in x-coordinates = 220 - 0 = 220
Length = difference in y-coordinates = 260 - 10 = 250
To find the center of the ceiling, we need to find the centroid (center-point) of the rectangle.
x-coordinate = Half of the width + smallest x-coordinate= (220 ÷ 2) + 0 = 110
y-coordinate = Half of the length + smallest y-coordinate = (250 ÷ 2) + 10 = 135
Therefore, the center of the ceiling is at (110, 135)
Please help! 15 Points.
1. Write the general term and pattern rule for the following pattern:
9, 6, 3, 0, -3
Then: Find the 15th, 25th, and 100th term values.
2. Write the general term and pattern rule for the following patterns: -7, -17, -27, -37, -47
Then: Find the 15th, 25th, and 100th term values.
Answers
Grandma baked 1.5 times as many pancakes as waffles. After she baked 45 more waffles, and her grandchildren ate 12 pancakes, there were 17 more waffles than pancakes. How many waffles were there initially?
PLS HELP YOU WILL GET BRAINLY!!!
Answers
Step-by-step explanation:
let x represent the no of pancakes,
she baked 1.5 times pancakes more than waffles,
so from this, no of pancakes = 1.5x,
then she baked more 45 waffles,
no of waffles = (x +45)
so you had 1.5x pancakes and the children ate 12 out of them. the no of pancakes has then been reduced by 12.
thus, no of pancakes = ( 1.5x -12 )
now they see that they have 17 more waffles that pancakes left. this means that :
no of waffles - no of pancakes = 17
(x+45) - (1.5x - 12) = 17
x - 1.5x + 45 + 12 = 17
x = -50 / -0.5
x = 100
hence, there were 100 waffles initially.
hope you understand this,
-s.
Tatiana reads 40 pages of her book every night for x number of nights. write and expression that repressents the number of pages eh read
Answers
Answer: 40x
Step-by-step explanation:
Titiana read 40 pages of her book every night for x number of nights, which means she read 40 pages every day. So 40 times x is how many pages she read in all.
I need help on this other question sry if it is hard... here is the pic.
Answers
Answer:
142%
Step-by-step explanation:
i may be wrong but hopefully im not!!
Answer:
142%
Step-by-step explanation:
To change a fraction to a percentage, multiply it by 100%
1 [tex]\frac{21}{50}[/tex] ( change to an improper fraction )
= [tex]\frac{71}{50}[/tex] × 100% = 71 × 2 = 142%
6) the cost of a video game is $22.00
Sales tax is 6%
How much will the game cost, including tax
Answers
Answer:
$23.32
Step-by-step explanation:
which of these functions has the highest midline?
a) 1-sin(t+3pi/2),
b) 2-sin(t/2 + pi/4),
c) sin(2t- pi/2),
d) 2sin(t-pi)
Answers
Ann purchased a DVD player on sale. The initial price was $175.90. The price after the discount was $150.75. What was the percent of decrease (discount rate)?
Answers
Answer:
14.29% decrease (actual : 14.2979%)
What is the perimeter of a pentagon with side length 35cm?
Answers
Answer:
175 cm
Step-by-step explanation:
35 x 5 = 175
HELP Given f(x) = 4x2 – 3x – 6, what is the value of f(-1)?
A. -7
B. 2
C. -5
D. 1
Answers
Answer:
D) 1
Step-by-step explanation:
Given f(x) = 4x² - 3x - 6
f(-1)=4(-1)² -3 (-1) -6
f(-1)= 4+3-6
f(-1)= 1
Hope it helps! :)
Based on the information in this table, which equation can be used to model the relationship between x and y?
Question 6 options:
y = 5x + 2
y = 2x
y = 2x + 5
y = 5x
Answers
Take 2 points
(6,17)(7,19)Slope:-
[tex]\\ \tt\hookrightarrow m=\dfrac{19-17}{7-6}=2[/tex]
Equation in point slope form
[tex]\\ \tt\hookrightarrow y-17=2(x-6)[/tex]
[tex]\\ \tt\hookrightarrow y-17=2x-12[/tex]
[tex]\\ \tt\hookrightarrow y=2x+5[/tex]
-All of the following are phases (states) of matter EXCEPT:
Answers
Answer:
The states of matter are solid, liquid, gas, and plasma
Step-by-step explanation:
you didn't have any options so I'm just telling you them
5
How can you classify quadrilaterals? Explain using properties of sides and angles.
(Be sure to write at least 5 complete sentences)
Answers
Answer:
A quadrilateral is a polygon with four sides. A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. A rhombus is a parallelogram with four congruent sides. A trapezoid is a quadrilateral with exactly one pair of parallel sides. A kite is a quadrilateral with exactly two pairs of adjacent congruent sides. And A scalene quadrilateral is a four-sided polygon that has no congruent sides. Three examples are shown below.
Step-by-step explanation:
I hope this helps, I also couldn't find a answer :D