Write the complex number in trigonometric form.
z = 5 - 5i

Answers

Answer 1

Answer:

[tex] \large \boxed{ \boxed{ \red{ \ \rm 5 \sqrt{2} ( \cos( \dfrac{7\pi}{4} ) + i \sin( \dfrac{7\pi}{4} ) )}}}[/tex]

Step-by-step explanation:

to understand thisyou need to know about:imaginary numberPEMDAStips and formulas:[tex] \sf \: formula \: of \: trigonometric \: form : \\ \rm r( \cos( \theta) + i \sin( \theta) )[/tex][tex] \rm \: r = \sqrt{ {a}^{2} + {b}^{2} } [/tex][tex] \rm \theta = \arctan( \dfrac{b}{a} )[/tex]given:z=5-5ilet's solve:

complex number:a+bi

therefore

our a is 5our b is -5

[tex] \sf sustitute \: the \: value \: of \: a \: and \: b \: into \: the \: modulus : [/tex]

[tex] \rm \: r = \sqrt{ {5}^{2} + ( { - 5)}^{2} } [/tex]

[tex] \sf simplify \: squres : [/tex]

[tex] \rm \: r = \sqrt{25 + 25} [/tex]

[tex] \sf simplify \: addition : [/tex]

[tex] \rm \: r = \sqrt{50} [/tex]

[tex] \sf rewrite \: 50 \: as \: 2 \times 25[/tex]

[tex] \sf r = \sqrt{2 \times 25} [/tex]

[tex] \sf use \: \sqrt{ab} \iff \: \sqrt{a } \sqrt{b} : [/tex]

[tex] \rm r = \sqrt{25} \sqrt{2} [/tex]

[tex] \therefore \rm \: r = 5 \sqrt{2} [/tex]

[tex] \sf sustitute \: the \: value \: of \: a \: and \: b \: into \: the \: agrument : [/tex]

[tex] \rm \theta = \arctan(\dfrac{ - 5}{5} )[/tex]

[tex] \sf simplify \: divition : [/tex]

[tex] \rm \theta = \arctan( - 1)[/tex]

[tex] \theta = - \dfrac{\pi}{4} [/tex]

[tex] \sf add \: 2\pi \: to \: get \: a \: positive \: agrument[/tex]

[tex] \rm \theta = - \dfrac{\pi}{4} + 2\pi \\ \rm\therefore \: \theta = \frac{7\pi}{4} [/tex]

[tex] \sf \: sustitute \: the \: value \: of \: \rm \: r \: and \: \theta : \\ \rm 5 \sqrt{2} ( \cos( \frac{7\pi}{4} ) + i \sin( \frac{7\pi}{4} ) )[/tex]

[tex]\text{And we are done!}[/tex]


Related Questions

please help if you can <3

Answers

Answer:

1) x = 71

2) x = 117

5)

m<1: 35

m<2: 77

m<3: 52

m<4: 77

m<5: 65

m<6: 25

Step-by-step explanation:

1)

x + 41 + 68 = 180

x + 109 = 180

x = 71

2)

x + 47 + 16 = 180

x + 63 = 180

x = 117

3)

<2 + 103 = 180

<2 = 77

<1 + 68 + 77 = 180

<1 + 145 = 180

<1 = 35

<4 + 103 = 180

<4 = 77

<5 + 41 + 77 = 180

<5 + 115 = 180

<5 = 65

<6 + 65 = 90

<6 = 25

<3 + 103 + 25 = 180

<3 + 128 = 180

<3 = 52

Which of the following statement(s) describes the rate of change of f over the interval 1.5 SXS 3? Select all that apply.

A. The rate of change is 1/2

B. The rate of change is 2

C. The rate of change is constant

D. The rate of change is increasing

Answers

The answer is going to be C

Segment MP is a diameter of circle O.


Circle O is shown. Line segment M P is a diameter. Line segment N O is a radius. Angle N O P is 150 degrees.


Which equation can be used to find mArc M N?

mArc M N – 150 = 360

Answers

Answer:

[tex]arc\ MN + 150 = 180[/tex]

Step-by-step explanation:

Given

[tex]\angle NOP = 150^\circ[/tex]

See attachment for circle O

Required

Find [tex]arc\ MN[/tex]

The sum of angles in a semi-circle is 180 degrees.

So:

[tex]arc\ MN + \angle NOP = 180[/tex]

This gives:

[tex]arc\ MN + 150 = 180[/tex]

Hence, the equation is: [tex]arc\ MN + 150 = 180[/tex]

Answer:

A

Step-by-step explanation:

just took exam and got 100%

How many moles is 1.50 X 10^23 molecules NaCl ?

Answers

Answer:

One mole NaCI

hope it help :)

This data represents the number of books checked out of the school library by five students: 10, 15, 5, 10, 20 Find the mean absolute deviation. FIRST PERSON TO ANSWER GET BRAINLIEST!

Answers

Answer:

the answer is 12

Step-by-step explanation:

you are welcome

Answer:

12......................

Rope packaged in 80-foot lengths
must be cut into 12-foot pieces to
do a certain job. If 28 such pieces
of rope are needed for the job, how
many packages of rope are needed?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 28

Answers

Answer:

it would be 5

Step-by-step explanation:

any of the answer could have really worked (not 4 since that gives you less then what is needed) but in the end it would have been 5 because 5 leaves you with only 5.33 feet of rope left

80* any one of the four numbers (ex: 5) = your answer that you got (ex: 400)

then you divide that number by 28 (ex: 33.33) and if you want to go the extra mile then do the number that you got by dividing 28 minis the number of rope pieces needed

the whole thing >

80* 5 = 400

400/28 = 33.33

33.33- 28 = 5.33

hope this helps! :)

Carlos and Bonita were just hired at a manufacturing plant. Carlos will earn $12.50 per hour. He will earn a hiring bonus of $300. Bonita will earn $14.50, but she will not get a hiring bonus. After how many hours of working will they earn the same?

Answers

Answer:

after 3 hours

Step-by-step explanation:

through: (0,3), parallel to y= -2x + 4

Answers

the slope is -2 because y = mx + b

y-y₁ = m (x-x₁)

y - 3 = -2 (x-0)

y - 3 = -2x

y = -2x + 3

Ella ran 6 times around her school building. then she ran 4 miles home. Her phone told her she ran 7 miles total. Which equation represents this situation A. 6+4x=7 B. 6x+4=7 C. 6(x+4)=7

Answers

hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

how do you work out standard form in maths

Answers

Answer:

ok

Step-by-step explanation:

is that you write down 1 and 10 then you write x10 to the power of a number

PLEASE HELP THANK U SO MUCH

Answers

Answer:

Add the area of the rectangle to the area of the triangle.

6 x 7 = 42

3 x 6 x 0.5 = 9

So the area is 42+9=51

Let me know if this helps!

it's 51! just got this correct.

You get to fill a bag with any type of candy for $1.35 per gram. You get to the counter ad have 5.23 grams of candy. How much do you have to pay?

Answers

Answer:

about $7.06

Step-by-step explanation:

Answer:

$7.06

Step-by-step explanation:

unit cost: $1.35/gram

5.23 grams * $1.35/gram = $7.0605

Answer: $7.06

convert $98.60 to pounds

Answers

Answer:

71.18 pounds

Step-by-step explanation: HOPE THIS HELPS

Can someone plz help me plzzzz I’m being timed

Answers

19,21,23,25 easy hope this help you good luck in time

Answer:

1 = 19.     3 = 21.     7 = 25

Step-by-step explanation:

w = t + 18

19 = 1 + 18

21 = 3 + 18

25 = 7 + 18

2/17=X/9


what does x equal??

Answers

Answer:    Multiply to remove the fraction, then set equal to  

0

and solve.

Exact Form:

X  =  18 /17

Decimal Form:

X  =  1.05882352 …

Mixed Number Form:

X  =  1 1 /17

2

17

=

X

9

what does  

x

equal??

Multiply both sides of the equation by  

9

.

2

17

9

=

X

9

9

Simplify.

Tap for more steps...

18 /17  =  X

Rewrite the equation as  

X  =  18 /17 .

X  =  18 /17

The result can be shown in multiple forms.

Exact Form:

X  =  18 /17

Decimal Form:

X  =  1.05882352 …

Mixed Number Form:

X  =  1   1 /17

Step-by-step explanation:

2/17=X/9

what does x equal??

There are 8 shirts in your closet, 4 blue shirts and 4 green shirts. You randomly select one to wear on Monday and then a DIFFERENT one on Tuesday. What is the probability you will wear blue on both days?

Question 8 options:

A. 5/14

B. 1/4

C. 1/2

D. 3/14

Answers

Answer:

1/4

Step-by-step explanation:

1/4 ‏‏‎ ‎ ‏‏‎ ‎ ‏‏‎ ‎ ‏‏‎ ‎​

PLS HELP: SEVENTH GRADE MATH

Answers

Answer:x=15

Step-by-step explanation:3x15=45

45+45=90

x=15
45 divided by 3 equals 15

19. Mr. Green teaches band, choir, and math. This year, he has 57 students that take at least one of (3 points)
his classes. He teaches band to 25 students. There are 9 students who have Mr. Green for math
and nothing else. Use the Venn diagram below:
Math
7
3
11
17
Band
Choir
How many students take exactly 2 classes with Mr. Green?

Answers

Answer:

The answer is "17 students with Mr. Green take exactly two courses".

Step-by-step explanation:

Following are the calculation to this question:

Alone band 11

Alone chorus 17

Choir and band alone 4

7 Maths alone and the band

Choir and Math alone 6

Chorus and Math Band 3

mathematics alone 9 +11+4+10+6+17  + M = 57

so

2 classes = 4+7+6 = 17

So, there are 17 students with Mr. Green take exactly two courses.

6. Find the constant of variation k for the direct variation.
4x = -y
K = -1
K=-1/4
K=4
K=-4

Answers

Given:

The equation for the direct variation is

[tex]4x=-y[/tex]

To find:

The constant of variation k for the direct variation.

Solution:

If y is directly proportional to x, then

[tex]y\propto x[/tex]

[tex]y=kx[/tex]        ...(i)

Where, k is constant of variation or constant of proportionality.

We have,

[tex]4x=-y[/tex]

It can be written as

[tex]-y=4x[/tex]

Multiply both sides by -1.

[tex]y=-4x[/tex]      ...(ii)

On comparing (i) and (ii),we get

[tex]k=-4[/tex]

Therefore, the correct option is D.

Find the median for the following set of numbers.
4, 18, 3, 29, 23
0 29
3
18
04

Answers

Answer:

3 is the median

Step-by-step explanation:

the median is just the middle number, the number in the middle of a sequence

3 is perfectly in the middle

hope this helps chu <3

Anyone know this ???

Answers

Answer:

The answer is D

Step-by-step explanation:

Have a great day

9. Which
of the following is a proper fraction?
A 12/10
B. 5/4
C.7/10
D.10 1/9​

Answers

Answer:

c

Step-by-step explanation:

because in a proper fraction the numerator is less than the denominator

The product of a binomial and a trinomial is x3+3x2-x+2x2+6x-2 Which expression is equivalent to this
product after it has been fully simplified?

Answers

The answer is the first one.
Explanation:
X^3 stays the same because there are no other cubed numbers in the problem
Next you combine the x^2s
The x^2s are +3x^2 and +2x^2
Since they are both positive, you add them: 3x^2 + 2x^2 = 5x^2
Next you do the x values
-x and +6x, also known as 6x - x = 5x
Lastly, you just add in the -2 and get:
X^3 + 5x^2 + 5x - 2

A cylinder has a volume of 36 cubic inches. What is the volume of a cone if it has the same radius and height as the cylinder?

Answers

Answer:

12 cubic inches

Step-by-step explanation:

volume of a cylinder= pi*r2*height

but we are given 36 as cylinder volume.

Therefore , 36 = pi*r2* height

r2*height = 36/pi, let call this equation 1

volume of a cone = pi*r2*height/3;

but from equation 1, r2*height =36/pi, substituting this value in volume of cone.

volume of cone= pi*(36/pi)/3 = 12 cubic inches

There are 25 headsets, 8 of them are not working properly. Find the percentage of headsets that are in good quality.

Answers

Answer:

68%

Step-by-step explanation:

Given data

Number of Headset= 25

Number of bad Headset= 8

Percentage of bad Headset= 8/25*100

=  0.32*100

= 32%

Hence the percentage of good Headset is

=100-32

=68%

Pls help I’ll give brainliest

Answers

Answer:

B)  7 gallons

Step-by-step explanation:

car begins with 12 gallons and, at a rate of 29 mpg, would allow the car to travel for 348 miles

car only traveled 140 miles so 208 miles more can be driven

208÷29 is approx 7 gallons

A cable company uses the formula S = 20,000 (1 + 0.08)^y to estimate the number of subscribers, S, that use their service after y years. If there were 20,000 cable television subscribers when the cable company began, what is the meaning of the expression (1 + 0.008) ^y?

Answers

Answer:

the expression above is

y = Subscribers after time t = S

a = Initial Subscribers =20,000

r = Growth rate = 0.08 = 8%

t = time in years = y

Step-by-step explanation:

A cable company uses the formula S = 20,000 (1 + 0.08)^y to estimate the number of subscribers, S, that use their service after y years. If there were 20,000 cable television subscribers when the cable company began, what is the meaning of the expression (1 + 0.008) ^y?

The above question represents Exponential growth

Exponential growth formula =

y = a( 1 + r) ^t

Where:

y = Population after time t

a = Initial Population

r = Growth rate

t = time in years

S = 20,000 (1 + 0.08)^y

Hence, the expression above is

y = Subscribers after time t = S

a = Initial Subscribers =20,000

r = Growth rate = 0.08 = 8%

t = time in years = y

Can somone please help me and explain very much appreciated and this is 7th grade math btw

Answers

Answer:

4 8.95h + 10 < 115

Step-by-step explanation:

Answer: 4) 8.95h + 10 < 115

Step-by-step explanation:

We know the inequality will be equal to less than 115 since it states that the order was less than $115.

The equation would look like: some amount of shin guards times 8.95 each + $10 shipping = less than $115

8.95h + 10 < 115

(h in the given equation is the amount of shin guards)

Pls help ASAP fast ...

Answers

i donk know                       Step-by-step explanation:

Answer:

Here is your answer

Step-by-step explanation:

How many degrees is angle A? ​

Answers

Answer:

128 degrees

Step-by-step explanation:

Answer:  112 degrees

============================================================

Explanation:

If we assume ABCD is a parallelogram, then the adjacent angles are supplementary.

So,

A+D = 180

A+68 = 180

A = 180-68

A = 112

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