Answers
So, its more like this:
Using the polar form, a complex number with modulus r and argument θ may be written
z = r(cos 0 + j sin θ)
It follows immediately from Euler’s relations that we can also write this complex number in
exponential form as :
z = [tex]re^{j0}[/tex]
When using this form you should ensure that all angles are measured in radians and not degrees.
The exponential form of a complex number is in widespread use in engineering and science. Since z = r(cosθ + isinθ) and since eiθ = cosθ + isinθ we therefore obtain another way in which to denote a complex number: z = reiθ, called the exponential form.
I'm leaning towards the answer choices A. and C.
But I'm sure it's A because of the two, C has an x. That's the only difference they have.
Here's another example,
Let z=x+iy, its exponential form comes from identifying it as the point (x,y) in the (Argand) plane. This basically amounts to writing it in what would be polar form in the real plane. Writing it as:
z =reiθ
. If you graph the point (x,y) and treat it as a vector its easy to see that r=|z| and θ=tan−1(yx).
For purely real numbers, they are already in exponential form since they are equal to their modulus and θ=0.
Also, you can write:
Re(z)=z+z¯2
if you want to write it purely in terms of z. Both of your numbers are purely real and thus they are already in exponential form. I suppose if you wanted to be strict about it you could write it as:
|1−z|=|1−z|e0i
Related Questions
Help please (NO LINKS ASAP AND NO RANDOM THINGS)
Answers
Answer: the answer is 13
Step-by-step explanation:
Martina is on the swim team. Each week she swims a total of 8,000 meters. How many kilometers does she swim each week?
Be sure to include the correct unit in your answer
Answers
Answer:
She swims 8 kilometers a week 8KM
Step-by-step explanation:
Write the linear equation that gives the rule for this table.
Answers
Answer:
f(x) = -7x + 1
Step-by-step explanation:
Slope intercept form is
y = mx + b
m is slope
b is y-intercept
--------------------------
y decreases by 7 for each increase of 1 in x
slope = -7
to find "b" plug in one of the points and m = -7
using point (3, -20)
y = mx + b
-20 = -7(3) + b
-20 = -21 + b
b = 1
The equation is
f(x) = -7x + 1
PLEASE HELP
On the graph below, Point A is located at the intersection of angle θ and the unit circle.
What are the exact coordinates of point A?
Use the on-screen keyboard to type the answer in the box below.
https://imgur.com/a/UwbnsCV
Answers
Answer:
1/2,
Step-by-step explanation: Please find the attached image of unit circle.
We have been given that the measure of angle t is 60 degrees. We are asked to find the x-coordinate of the point where the terminal side intersects the unit circle.
We know that x-coordinate on unit circle represents cosine and y-coordinate represents sine of a given angle.
We can see from our attachment that x-coordinate of the point at angle 60 degrees is , therefore, x-coordinate of the angle of 60 degrees, where the terminal side intersects the unit circle is .
Haley is going on a vacation to Australia. Her flight leaves at 10:20 A.M. It takes 1 hour and
20 minutes to get to the airport, and Haley wants to be at the airport 55 minutes before her
flight leaves. What is the latest time that Haley can leave for the airport?
HELPPPPP FACTUAL ANSWERS
Answers
Answer:
8:05 am is the time she will have to leave her house to get to the airport on time.
Step-by-step explanation:
First, subtract 55 minutes from 10:20.
10:20 - 20 = 10:00
10:00 - 35 = 9:25
This is the time she wants to arrive. 9:25
Now, we have to subtract an hour and 20 minutes
9:25 - 1:00 = 8:25
8:25 - 20 = 8:05
Hope this helped and have a great day! :)
i need find volumen i need help
Answers
Answer:
it's 512
Step-by-step explanation:
I need help on dis one
Answers
Answer:
B, C, and D
Step-by-step explanation:
ahhhhh uh you are looking for things less than that line so you would pretty much shade in the under side of the line and any point that is in that shaded region is the answer
A rectangular rug has an area of 84 square feet. If the length is 8 feet more than the width, find the dimensions of the rug.
Answers
Answer:
w=6
l=14
Step-by-step explanation:
Area of rectangle = l*w
So:
[tex]w*(w+8)=84[/tex]
Then, just find w, and w+8.
[tex]w^2+8w=84\\w^2+8w-84=0\\(w-6)(w+14)=0\\w-6=0, w=6\\w+14=0, w=-14[/tex]
Length cannot be negative, so the width is 6.
Length = width + 8 = 6+8=14
Consider the following question: How many years has each person played on the soccer team? Which best describes the question? It is a statistical question because the data may vary for each player. It is a statistical question because the data will all be the same. It is not a statistical question because the answers are all whole numbers. It is not a statistical question because there is only one answer per person.
Answers
Answer:
Its the first one
Step-by-step explanation:
It is a statistical question because the data may vary for each player. :)
13. Car Depot rents a car for an initial fee of $20
plus an additional $0.10 per mile. Model the
total cost of the rental car C as a function of the
number of miles driven m.
a
a. C(m) = .10(20m)
b. C(m) = m(20+.10)
C. C(m) = 20m +.10
d. C(m) = .10m + 20
2
Answers
Answer:
d. C(m) = .10m + 20
Step-by-step explanation:
Given the following data;
Initial rent fee = $20
Cost per mile = $0.10
To find the total cost;
The total cost is simply the sum of the initial rent fee and the cost per mile of the car.
Mathematically, the total cost is given by the expression;
T = I + cm
Substituting into the above formula, we have;
T = $20 + 0.10m
Convert the polar representation of this complex number into its rectangular
form:
z = 4(cos pi/2 + i sin pi/2)
Please help!!! I will mark brainliest!!! Thank you!!!
Answers
Answer: (0,4)
Step-by-step explanation:
The complex number z = 4 into its rectangular form
What is complex number?Every complex number may be represented in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element labeled I sometimes known as the imaginary unit, and satisfying the equation i² = 1.
Given
* Lets revise the complex numbers
- If z = r(cos Ф ± i sin Ф), where r cos Ф is the real part and i r sin Ф is the imaginary part in the polar form
- The value of i = √(-1) ⇒ imaginary number
- Then z = a + bi , where a is the real part and bi is the imaginary part
in the rectangular form
∴ a = r cos Ф and b = r sin Ф
* Lets solve the problem
∵ z = r (cos Ф ± i sin Ф)
∵ z = 4 (cos π/2 + i sin π/2)
∴ The real part is 4 cos π/2
∴ The imaginary part is 4 sin π/2
- Lets find the values of cos π/2 and sin π/2
∵ The angle of measure π is on the positive part of x axis at the
point (0 , 4)
∵ x = cos π/2 and y = sin π/2
∴ cos π/2 = 0
∴ sin π/2 = 1
∴ a = 4(0) = 0
∴ b = 4(1) = 4
∴ z = 0 + i (4)
* The complex number z = (0,4) into its rectangular form
To learn more about complex numbers refer to:
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HELP IF RIGHT I WILL MARK BRAINLIEST!!!! TRUST
Answers
Answer:
I came up with 412cm^2
Step-by-step explanation:
10*12+(12*2)2+(10*2)2+6*8+(8*3)2+(6*3)2+(12*10-6*8)
A person invests 1000 dollars in a bank. The bank pays 4% interest compounded
quarterly. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 1600 dollars
A=P(1+)
"
Sant Pere
Answers
Answer:
The person must leave the money for 11.8 years until the investment reaches 1600 dollars.
Step-by-step explanation:
Given that a person invests 1000 dollars in a bank, and the bank pays 4% interest compounded quarterly, to determine to the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 1600 dollars the following calculation must be done:
1000 x (1 + 0.04 / 4) ^ Xx4 = 1600
1000 x 1.01 ^ 4X = 1600
1010 ^ 4X = 1600
X = 11.8
Therefore, the person must leave the money for 11.8 years until the investment reaches 1600 dollars.
A right-angled triangle, with two sides adjacent to the right angle labeled 7 and 11 respectively, and the hypotenuse is labeled x.
Find the exact value of $x$ .
Answers
Answer:
170
c=a^2+b^2=7^2+11^2≈13.0384 or 170
Step-by-step explanation:
mrk me brainliest please
iihhhhhhhhhhhhhhhhhhhhiiiiiiiiiiii
Answers
Answer:
hhhhhhhhhhhhhhhhhhhiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
Step-by-step explanation:
There were 104 females and 78 males present at the high school pep rally. Find the ratio of males to the total number of people present in simplified form
Answers
yeah that’s they answer i got
I need he answer pls {WIIL MARK BRAINLIST}
Answers
Answer:
B. {2, 5, 6, 9}
Step-by-step explanation:
Mean: the sum of all numbers divided by the amount of numbers.
Median: The number between the two middle numbers
-------------------------------------------------------------------------------------------------
Mean: {2 + 5 + 6 + 9} = 22 ÷ 4 = 5.5.
Median: The median of this data set will be 5.5 because it is in between 5 and 6
You are walking 1 mile home from school. When you are halfway home, you realize that you forgot a book in your locker and have to go back and get it. Once you finally get home, how far have you walked?
Answers
Answer:
2 miles
Step-by-step explanation:
2 miles :)
(2.8•10^8)(1.9•10^4)
Answers
Answer: 5.32 × 10^12
Step-by-step explanation:
This is a question relating to indices. In indices, we add the power given for question relating to multiplication. Hence, this will be:
= (2.8•10^8)(1.9•10^4)
= (2.8 × 1.9) × 10^8+4
= 5.32 × 10^12
Therefore, the answer to the question will be 5.32 × 10^12.
If g(x)= -(3/(4x)) , find g(g(x)) please show work.
Answers
Answer:
[tex] g(g(x)) = x [/tex]
Step-by-step explanation:
[tex] g(x) = -\dfrac{3}{4x} [/tex]
[tex] g(g(x)) = -\dfrac{3}{4g(x)} [/tex]
[tex] g(g(x)) = -\dfrac{3}{4(-\frac{3}{4x})} [/tex]
[tex] g(g(x)) = -\dfrac{3}{4} \div (-\frac{3}{4x}) [/tex]
[tex] g(g(x)) = -\dfrac{3}{4} \times (-\frac{4x}{3}) [/tex]
[tex] g(g(x)) = \dfrac{3 \times 4x}{4 \times 3} [/tex]
[tex] g(g(x)) = x [/tex]
Numerical expressions for add 12 to 8 then multiply by 5
Answers
Answer:
(12 + 8) x 5
Step-by-step explanation:
HELP ME PLEASEEEEEEEEEEEEEEEEEEE
Answers
The Unit Circle
For the given central angle, determine the distance traveled along the unit from the point (1. 0)
210°
a. 3.67 units
b. 1.17 units clockwise
c. 1.83 units
d. 7.33 units
Please select the best answer from the choices provided
Answers
Answer:
A. 3.67 units
Step-by-step explanation:
I calculated it logically
Write 18/n
as a verbal expression.
Answers
Answer:
18 divided by a N value
Step-by-step explanation:
5 + 14 x y = 9 x y - 5
Answers
Answer:
xy = -2
Step-by-step explanation:
To solve:
5 + 14xy = 9xy - 5
=> First subtract 9xy from each side of "="
5 + 5xy = -5
=> Now, subtract 5 from each side:
5xy = -10
=> Finally divide 5 on each side:
xy = -10/5
xy = -2
Hope this helps!
Identify all of the transformation effects on the graph of the function f(x) = x when f(x) is replaced with -f(x + 4) - 6.
A)
shifted up 6 units
B)
shifted down 6 units
shifted left 4 units
D)
shifted right 4 units
E)
reflected over x-axis
Answers
Answer: B,C E put as brainliest
Step-by-step explanation:
Find the volume of the cube below.
Answers
Answer :
3.5 × 3.5 × 3.5 = 42.875
Lana expected 50 people to come to the picnic, but 60 people actually showed up.
Calculate the percent error.
Answers
Answer:
it is 10%
Step-by-step explanation:
60 - 50 = 10
Solve for x 6x + 7 = 19x = 28
Help and I will give brainiest use the photo to answer. Please provide step by step answer explanation
Answers
I think X=6
Explanation:
If X was 6 that That would mean 6(6)+7=43 and 19(6)-28=86 Line 6x+7 is about half of line 19x-28 so that means that this right here would be the closest answer. 86/2=43 Hope that helps .
The value of x to satisfy the given case is 2.
What is mid point theorem?The mid point theorem states that in a triangle the line segment joining the mid point of two sides is always parallel and equal to half of the length of the third side.
As per the given figure the data is as follows,
The line segment of length 6x + 7 is parallel to the side of a triangle of length 19x - 28 such that it divides other two sides equally.
Apply mid point theorem to obtain,
6x + 7 = 1/2(19x - 28)
=> 19x/2 - 6x = 14 - 7
=> 7x/2 = 7
=> x = 2
Hence, the value of x for the given triangle is 2.
To know more about mid point theorem click on,
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In parallelogram ABCDwith diagonals AC and BD, which of the following is true?
Answers
Answer:
Last one at the bottom
Step-by-step explanation:
Because all of those diagonals are equal to each other. So that would mean those diagonals are equal in legnth.
BD is perpendicular to AC Because; all of those diagonals are equal to each other that would mean those diagonals are equal in length.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Remember that the parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.
The diagonals of the parallelogram are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).
BD is perpendicular to AC Because; all of those diagonals are equal to each other that would mean those diagonals are equal in length.
LEarn more about the parallelogram here;
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