What is 2 + 2i in polar form?
Answers
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The polar form of 2+2i is [tex]$2\sqrt{2}(\cos(\frac{\pi}{4}) + i\sin(\frac{\pi}{4}))$[/tex]
We are given that;
The complex number= 2+2i
Now,
To convert a complex number from rectangular form to polar form, we need to find its magnitude and argument.
The magnitude is the distance from the origin to the point (x, y) on the complex plane, and the argument is the angle between the positive x-axis and the line joining the origin and the point.
Using the Pythagorean theorem and the inverse tangent function, we get:
Magnitude = [tex]$\sqrt{x^2 + y^2}$[/tex]
Argument = [tex]$\tan^{-1}(\frac{y}{x})$[/tex]
Plugging in x = 2 and y = 2i, we get:
Magnitude = [tex]$\sqrt{2^2 + 2^2} = \sqrt{8} = 2\sqrt{2}$[/tex]
Argument = [tex]$\tan^{-1}(\frac{2}{2}) = \frac{\pi}{4}$[/tex]
Therefore, by pythagoras theorem answer will be [tex]$2\sqrt{2}(\cos(\frac{\pi}{4}) + i\sin(\frac{\pi}{4}))$[/tex].
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Related Questions
Write a polynomial function in factored form of least that the given zeros and a leading coefficient of 1.
1. -6, 3, 5
2. 2, -2, -6i
Write a polynomial function in standard form of least degree that have real coefficients, the given zeros, and a leading coefficient of 1.
3. -1, 1, 7
4. 3, -3, -2i
Answers
9514 1404 393
Answer:
p(x) = (x+6)(x-3)(x-5)p(x) = (x-2)(x+2)(x^2 +36)p(x) = x^3 -7x^2 -x +7p(x) = x^4 -5x^2 -36Step-by-step explanation:
Each root r gives rise to a binomial factor (x-r). Each complex root also has a conjugate root, so roots ±ri give rise to a binomial factor (x^2 +r^2).
__
1. p(x) = (x -(-6))(x -3)(x -5)
p(x) = (x+6)(x-3)(x-5)
__
2. p(x) = (x -2)(x -(-2))(x^2 +6^2)
p(x) = (x -2)(x +2)(x^2 +36)
__
If you want standard form, you can start with factored form, then multiply it out.
3. p(x) = (x -1)(x +1)(x -7) = (x^2 -1)(x -7) = (x^2 -1)x +(x^2 -1)(-7)
p(x) = x^3 -7x^2 -x +7
__
4. p(x) = (x -3)(x +3)(x^2 +2^2) = (x^2 -9)(x^2 +4)
p(x) = x^4 -5x^2 -36
Is this relation a function?
Answers
Answer:
yes though i am not completely sure
Step-by-step explanation:
What additional information could be used to prove that triangle XYZ is congruent to triangle Fe.g. using asa or aas check all that apply
Answers
answer: Answer: ∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE are the additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS. we need only one angle and side.
Answer:
its the first one and the last one ..that's the answer.
HELPPPPPPPPP!!!
What is z/
W
0-4 + 16i
O 6 + 10i
O 7+11i
O 8+2i
Answers
The value of z/w is, (8 + 2i)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The graph is shown in figure.
And, The point z = (6 + 10i)
The point w = (1 + i)
Now,
We can find the value of z/w is,
⇒ z/w = (6 + 10i) / (1 + i)
= (6 + 10i) (1 - i) / (1 + i) (1 - i)
= (6 - 6i + 10i - 10i²) / (1 - i²)
= (6 + 4i + 10) / (1 + 1)
= (4i + 16) / 2
= (8 + 2i)
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a boat traved 27 miles in 2 hours at this rate how many miles will the boat travel in 1/2 hour as a fractoin
Answers
Answer:
6 3/4 or 27/4
Step-by-step explanation:
(27 / 2) / 2 = 6.75
A bike travels 24 miles in 3 hours. How many miles will the bike travel in 12 hours?
Answers
Answer:
72
Step-by-step explanation:
24 / 3 = 8
so
8*7 = 72
Answer:
72
Step-by-step explanation
24 / 3 = 8
so
8*7 = 72
PLS answer fast!!!! I am literally in tears. Brainliest to the first person to answer it correctly
Answers
Answer:
-682
Step-by-step explanation:
I worked it out and got -682
Does -3 and -2 make a right triangle
Answers
Answer:
There is no such thing as negative distances. In order to do Pythagoras theorem you need to know which one is the hypotenuse
Explain: you can’t make a right triangle with negative numbers. Plz mark brainlest
can you help me with it please
Answers
Answer:
[tex] \frac{20}{29}[/tex]
Step-by-step explanation:
Equation of unit circle is:
[tex] x^2 + y^2 = 1[/tex]
Plug [tex] y = \frac{-21}{29}[/tex] in above equation.
[tex] x^2 + \bigg( \frac{-21}{29}\bigg)^2 = 1\\\\
x^2 + \frac{441}{841} = 1\\\\
x^2 = 1-\frac{441}{841}\\\\
x^2 = \frac{841-441}{841}\\\\
x^2 = \frac{400}{841}\\\\
x =\pm\sqrt{ \frac{400}{841}}\\\\
x =\pm\frac{20}{29}\\\\
[/tex]
Since, point P is in the fourth quadrant.
Therefore, x - coordinate should be positive.
[tex] \huge \red {\boxed {\therefore x =\frac{20}{29}}} \\\\
[/tex]
Simplify: 5 -3 • 5 5
25 8
25 -15
5 -3
5 2
Answers
W- 33 = 66 what is W
Answers
w is equal to 99 cause is u subtract 33 fro it it equals 66
Answer:
W = 99
Step-by-step explanation:
To solve W, you need to isolate W. Add 33 to both sides:
W-33=66
W=99
What is the value of the expression when x = 4 and y = 3?
3x² + 5y
A.27
B.38
C.63
D.159
Answers
Answer:
63
Step-by-step explanation:
3x^2+5y
Where X=4,Y=3
So
=3×4×4+5×3
=48+15
=63
So 63 is the answer
Answer:
C.63
Step-by-step explanation:
3x4²+5x3
4² = 16
3x16+5x3
Then
3x16 = 48
5x3 =15
48+15 equals 63
The answer is 63
Have a Good Day!!!!
Now given a rope hanging from the top of a pole. The end lying on the ground is 3 chi long. When tightly stretchedit is 8 chi from the bottom of the pole. Let x represent the height of the pole. Tell: how long is the rope and how high is the pole
Answers
Answer:
Height of the pole = 9.17 chi.
Length of the rope = 12.17 chi.
Step-by-step explanation:
Given that the rope is hanging from the top of a pole having height x chi and the portion of the rope lying on the ground is 3 chi.
So, the length of the rope= x + 3 chi.
Let AB represents the pole in the figure, and one end of the rope is at point A.
When the rope is tightly stretched, let C be the other end of the rope as shown in the triangle.
The length of the rope = AC.
\Rightarrow AC=x+3 chi.
Distance from the bottom of the pole, point A, to the other end of the pole, point B, is 8 chi.
So, BC=8 chi.
As the triangle ABC is a right-angled triangle, so by using Pythagoras theorem,
[tex]AC^2= AB^2+BC^2[/tex]
[tex]\Rightarrow (x+3)^2=x^2+8^2[/tex]
[tex]\Rightarrow x^2+6x+9=x^2+64[/tex]
[tex]\Rightarrow 6x=64-9=55[/tex]
[tex]\Rightarrow x=55/6=9.17[/tex] chi.
Hence, the height of the pole, [tex]AB=x=9.17[/tex] chi,
and the length of the rope, [tex]x+3=9.17+3=12.17[/tex] chi.
Daniel has 1615 Skittles stored in boxes. If there are 85 boxes, how many Skittles must go in each box?
Answers
Answer:
19
Step-by-step explanation:
While it's really easy to just divide, I'm sure your teacher wants an equation so:
1615=85x here x= skittle boxes
1615/85=x In this line you can use divide to cancel out the multiplication, giving you
x=19
Find the product
(3x+4y)(x+y)
Answers
Answer:
Step-by-step explanation:
(3x+4y)(x+y)
Solution=3x^2+4xy+3xy+4y^2
=3x^2+7xy+4y^2
Hcf 16 and 24 find ???
Answers
Answer:
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
First Of All We Have Factorize These Two Numbers And Then We Will Find Their Highest Common Factor
16–2×2×2×2
24–2×2×2×3
So The Highest Common Factor is 8
That's Because Both Can be Divided by 8 and 8 is their Highest Common diviser.
Hope This Helps
classify the triangle based off of the measurements of its sides 30m, 30m
Answers
Answer:
i got it
its an isosceles triangle bc two sides are equal.
Cleo buys 2/4 pounds of turkey. Tyler buys 1/2 pounds of turkey. Who buys more turkey? Pls explain.
Answers
Answer:
No one because They bought the same amount. 2/4 is equvalent to 1/2, meaning they both are half a pound. :)
Step-by-step explanation:
If this helps pls mark me brainliest
Have a great day :)
the cube_____of 27 is 3.
Answers
Answer:
3
Step-by-step explanation:
Answer:
the cube ROOT of 27 is 3.
Step-by-step explanation:
Tiffany took her friends out to dinner. If the dinner was $29.53 and she gave a 20% tip, how much money did she spend on dinner?
Answers
Answer: The answer is 35.43 because 29.53 times 20% is 5.90, so you add 5.90 to 29.53 to get 35.43.
I need help with Kumon math level I 187 B
Answers
Answer:
attached is the answer :)
Step-by-step explanation:
The length of the tangent AB is [tex]\sqrt{2a^{2}+2b^{2} }[/tex] if the radii of the largest circle is a and the radii of the smallest one is b.
What is the tangent?It is a line that touches a single point on the circle.
How to determine the length of that tangent?Firstly we have to draw a perpendicular from O to the radii of the smallest circle. In this way AOLB becomes a rectangle. We let the point where the bisector intersect the radii as L.
OA=a
Lb=a also
O'L=b-a
In triangle OLO' we use pythagoras to calculate the value of OL which wil then equal to AB so,
OL=[tex]\sqrt{(b-a)^{2}+(a+b)^{2} }[/tex]
=[tex]\sqrt{2a^{2}+2b^{2} }[/tex]
It will be the length of AB also.
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Find the slope of the roofof a home that rises 8 feet for every horizontal change of 24 feet
A.-3
B.-1/3
C.1/3
D.3
Answers
Answer:
(C).
Step-by-step explanation:
[tex]\frac{8}{24}[/tex] = [tex]\frac{1}{3}[/tex]
Answer:
1/3
Step-by-step explanation:
8/24
=1/3
Tell me if it's wrong
25 miles/hour =_meters/minute
Answers
1/4 es un decimal exacto
Answers
Answer:
0.25
Step-by-step explanation:
Decimal exacto
La parte decimal de un número decimal exacto está compuesta por una cantidad finita de términos.
Ejemplos:
15.125
0.1
3.0000001
Si en sus factores sólo aparecen 2, 5 o ambos, la fracción es decimal exacta.
A(n) ______ shows relationships between things you are comparing.
Venn diagram
whole number
integer
Answers
Answer:
Venn Diagram
Step-by-step explanation:
Its a graph that's used in listing similarities and differences the other two aren't graphs but math terms
Gavin has a box of crayons. There are four purple crayons, three black crayons, three blue crayons, and two red crayons. What is the probability Gavin will draw a purple crayon put it on the table and then draw another purple
Answers
Answer:
4/12
Step-by-step explanation:
Select the correct answer. Given:In quadrilateral WXYZ , and bisect each other at point A. Prove: Quadrilateral WXYZ is a parallelogram. Statement Reason 1. and bisect each other. given 2. WA = YA XA = ZA definition of bisection 3. m∠YAZ = m∠XAW Vertical Angles Theorem 4. SAS criterion for congruence 5. ∠ YWX ≅ ∠WYZ Corresponding angles of congruent triangles are congruent. 6. || converse of Alternate Interior Angles Theorem 7. m∠XAY = m∠ZAW Vertical Angles Theorem 8. ∆XAY ≅ ∆ZAW SAS criterion for congruence 9. ∠XZW ≅ ∠ZXY Corresponding angles of congruent triangles are congruent. 10. || converse of Alternate Interior Angles Theorem 11. Quadrilateral WXYZ is a parallelogram. definition of parallelogram What is the missing statement in this proof? A. ∆XWY ≅ ∆ZYW B. ∆YAZ ≅ ∆WAX C. WY = XZ D. ||
Answers
Answer:
YAZ WAX is the answer...i couldn't put it as its shown on the problem but its the same letters
Step-by-step explanation:
i took the test and got 5/5....this answer was correct
Help please! I’ll give brainliest!
Answers
Answer:
i think the answer is B
i am sorry if this is wrong
Step-by-step explanation:
Suppose a stock drops in value by 60% one week, then increases in value the next week by 75%. Is the value higher or lower than where it started
Answers
Answer:
Lower
Step-by-step explanation:
Use the number 100 to see how the value changes:
First, calculate the 60% drop:
100(0.4)
= 40
Then, calculate the 75% increase:
40(1.75)
= 70
So, since 70 is smaller than 100, the value is lower than where it started.
Gina wants to make
hamburgers for 12 people.
Her recipe serves 8 people
and calls for 4.5 pounds of
ground beef. How much
ground beef should
Gia purchase?
h
Answers
Answer:
6.75 pounds
Step-by-step explanation:
This question is of direct variation. We will use x as our answer. 8 is 2/3 of 12, so 4.5 should be 2/3 of x. We can now make an equation.
[tex]4.5=\frac{2}{3} x\\4.5*\frac{3}{2} =\frac{2}{3} x*\frac{3}{2} \\6.75=x[/tex]
In order to solve the equation, we multiply both sides by the reciprocal of 2/3, which is 3/2.
* stands for multiplication
From solving our equation, we get 6.75. We can't forget the units, so the answer is 6.75 pounds.