What is the square root of -2i?

Answers

Answer 1

Answer:

1-i and -1+i

Step-by-step explanation:

We are to find the square roots of [tex]z=0-2i[/tex]. First, convert from Cartesian to polar form:

[tex]r=\sqrt{a^2+b^2}\\r=\sqrt{0^2+(-2)^2}\\r=\sqrt{0+4}\\r=\sqrt{4}\\r=2[/tex]

[tex]\theta=tan^{-1}(\frac{b}{a})\\ \theta=tan^{-1}(\frac{-2}{0})\\\theta=\frac{3\pi}{2}[/tex]

[tex]z=2(\cos\frac{3\pi}{2}+i\sin\frac{3\pi}{2})[/tex]

Next, use the formula [tex]\displaystyle \sqrt[n]{r}\biggr[\cis\biggr(\frac{\theta+2\pi k}{n}\biggr)\biggr][/tex] where [tex]\displaystyle k=0,1,2,...\:,n-1[/tex] to find the square roots:

When k=1

[tex]\displaystyle \sqrt[2]{2}\biggr[cis\biggr(\frac{\frac{3\pi}{2}+2\pi(1)}{2}\biggr)\biggr][/tex]

[tex]\displaystyle \sqrt{2}\biggr[cis\biggr(\frac{3\pi}{4}+\pi\biggr)\biggr][/tex]

[tex]\sqrt{2}\biggr(cis\frac{7\pi}{4}\biggr)[/tex]

[tex]\sqrt{2}(\cos\frac{7\pi}{4}+i\sin\frac{7\pi}{4})\\ \\\sqrt{2}(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i)\\ \\1-i[/tex]

When k=0

[tex]\displaystyle \sqrt[2]{2}\biggr[cis\biggr(\frac{\frac{3\pi}{2}+2\pi(0)}{2}\biggr)\biggr][/tex]

[tex]\sqrt{2}\biggr(cis\frac{3\pi}{4}\biggr)[/tex]

[tex]\sqrt{2}(\cos\frac{3\pi}{4}+i\sin\frac{3\pi}{4})\\ \\\sqrt{2}(-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i)\\ \\-1+i[/tex]

Thus, the square roots of -2i are 1-i and -1+i


Related Questions

From a set of whole numbers from 1 to 32, what is the probability of randomly choosing a number either divisible by 5 or divisible by 3?
A) 1/2
B) 7/16
C)15/32
D)5/8

Answers

Using it's concept, it is found that the probability of randomly choosing a number either divisible by 5 or divisible by 3 is given by:

B) 7/16

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem:

There is a total of 32 numbers.Those that are divisible by 3, 5 or both are: {3, 5, 6, 9, 10, 12, 15, 18, 20, 21, 24, 25, 27, 30}, that is, 14 numbers.

Hence the probability is given by:

p = 14/32 = 7/16.

More can be learned about probabilities at https://brainly.com/question/14398287

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Calculate the perimeter of the figure shown below.
5 ft
5 ft
10 ft
18 ft

Answers

Answer:

48

Step-by-step explanation:

10+5+18+15

pls mark brainliest

Jevator has a weight limit of
7. There are 3 people inside
An elevator has a weight limit of 1 ton there are 3 people inside the elevator Each person weighs 150
pounds. How many more
Pounds can the elevator safely hold?
450 pounds
850 pounds
1,550 pounds
1,850 pounds

Answers

Answer:

i think it would be 1550?

Step-by-step explanation:

im pretty sure you add teh weight of the three people and convert it to one ton

Write an expression that shows 104.

Answers

Answer:

k + 104

Step-by-step explanation:

k + 104

In a pizza restaurant, you can get a basic pizza with two toppings: cheese and tomato.
You can also make up your own pizza with extra toppings. You can choose from four
different extra toppings: olives, ham, mushrooms and salami.
Ross wants to order a pizza with two different extra toppings.
How many different combinations can Ross choose from?

Answers

The number of different topping combination illustrates combination

Ross have 6 different topping combination to select from

The number of different combination

The given parameters are:

Extra toppings, n = 4

Toppings to select, r = 2

The number of extra topping that Ross can select is then calculated  using the following combination formula

Toppings = nCr

This gives

Toppings = 4C2

Evaluate the combination expression

Toppings = 6

Hence, Ross have 6 different topping combination to select from

Read more about combination at:

https://brainly.com/question/11732255

How do graphs help you understand the data?

Answers

Answer:

Sometimes, data can be better understood when presented by a graph than by a table because the graph can reveal a trend or comparison.

Circle Y has an area of 394.38cm ^ 2 . What is the circumference? Use 3.14 for pi Round to the nearest hundredth.

Answers

Answer:

70.38 cm

Step-by-step explanation:

π = 3.14

Area of a circle = πr^2

394.38 = πr^2

125.598726 = r^2

r = 11.2070837 cm

Circumference = 2πr

C = 70.3804856 cm

Find the midpoint of the line segment with end coordinates of:
(-2,-4) and (-1,-5)

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's use section formula ~

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{mx_2 + nx_1}{m + n} [/tex]

[tex]\qquad \sf  \dashrightarrow \:y = \dfrac{my_2 + ny_1}{m + n} [/tex]

And since mid point divides a line segment Into two equal parts, m : n = 1 : 1

so, take m = n = 1

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{(1 \times - 1)+(1 \times - 2)}{ 1+ 1} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{- 1- 2}{ 2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{ - 3}{ 2} [/tex]

Now, let's find y - coordinate ~

[tex]\qquad \sf  \dashrightarrow \:y = \dfrac{(1 \times - 5) + (1 \times - 4)}{1 + 1} [/tex]

[tex]\qquad \sf  \dashrightarrow \:y = \dfrac{ - 5 - 4}{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:y = \dfrac{ - 9}{2} [/tex]

So, coordinates of midpoint is ~

[tex]\qquad \sf  \dashrightarrow \:( - \dfrac{3}{2} ,- \dfrac{9}{2} )[/tex]

given that ax60=b work out the value of 4b/a

Answers

Answer:

Given,

a x 60 = b

or

b = a x 60

Similarly, the value of a would be:

We need to find

Therefore, we have to put the either values of a and b in the specified equation:

Hence,

We have only put the value of one variable to evaluate or to make it variable free

or

Therefore, the value of 4b/a​ is 240.

23, 92, 368, ..
Find the 6th term.

Answers

Answer:

6th term = 23,552

Step-by-step explanation:

Mutilyby 4 from left to right

368/92 =4---------------   92x4= 368

92/23=4--------------- 23x4 =92

1) 23

2) 23x4=    92

3) 92x4=386

4) 386x4=1,472

 ------and so on                          

Zachary is an engineer and studies trains. He found this interesting problem involving a passenger train and a freight train:

A passenger train left New York and traveled North while a freight left from the same place, at the same time and traveled South. After traveling for 6 hours the trains were 720 miles apart. If the passenger train was traveling at 80 mph, how fast was the freight train traveling

Answers

Answer:

40 m/hr

Step-by-step explanation:

6 hours * 80 m/hr      +     6 hours * x m/hr  = 720 miles

6 * 80     +    6 * x   = 720

x = 40 m/hr

HELP ASAP PLS the area of the circle is 64 pi square cm what is the radius of the circle in cm

Answers

Answer:

8cm

explanation:

let radius of circle be r

area of circle = 64π cm^2

π×r^2=64π

r^2=64 (cancel out π from both side)

r=√64 ( square root both side to remove the power from r)

r=8 cm

If 140 people were surveyed how many preferred crab? /////Show your work!

Answers

[tex]\qquad\qquad\huge \: \sf Answer[/tex]

Number of people who prefer crabs are :

[tex] \\qquad \tt \dashrightarrow \:{30\% \:\: of \:\: 140} [/tex]

[tex]\qquad \tt \dashrightarrow \: \dfrac{30}{100} \times 140 [/tex]

[tex]\qquad \tt \dashrightarrow \:3 \times 14[/tex]

[tex]\qquad \tt \dashrightarrow \:42 \: \: people[/tex]

What is the solution for 2.5x-5=5?

Answers

Answer:

Simplifying

2.5x + -5 = 5

Reorder the terms:

-5 + 2.5x = 5

Solving

-5 + 2.5x = 5

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.

-5 + 5 + 2.5x = 5 + 5

Combine like terms: -5 + 5 = 0

0 + 2.5x = 5 + 5

2.5x = 5 + 5

Combine like terms: 5 + 5 = 10

2.5x = 10

Divide each side by '2.5'.

x = 4

Simplifying

x = 4

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

2.5x-5=5

isolate the variable to find your answer

2.5x-5=5

      +5>+5

2.5x=10

divide by 2.5

10/2.5=4

x=4

A sphere has a radius 4 cm. What is its volume, to the nearest cubic cm? Write your answer to the nearest 10th place and use 3.14 for π???? HELPPPPP ASAP PLEASE!!!!!!!!!!!!!!!AND THANKS

Answers

Answer:

267.95

Step-by-step explanation:

Sphere Volume = 4/3 π r³

= 4/3 × 3.14 × 4³

= 803.84/3

= 267.94666...

= 267.95

What number has 6 tens and 1
more one than tens?

Answers

Answer:

17

Step-by-step explanation:

A. What is 0.47 expressed as a fraction in simplest form?

B. What is 0.-47 expressed as a fraction in simplest form?

C. What is 0.--47 expressed as a fraction in simplest form?

Please show your work for each part.

25 points! and Brainliest!

Answers

Answer:

See below ~

Step-by-step explanation:

Converting a decimal to a fraction :

Multiply by 100/100 and keep in the form without division

A. (0.47)

0.47 x 100/10047/100

B. (-0.47)

-0.47 x 100/100-47/100

C. (0.--47)

A minus sign multiplied by another minus sign makes a positive sign0.--47 ⇒ 0.4747/100

Answer:

Part (a) = 47/100, Part (b) = -47/100, Part (c) = 47/100

Step-by-step explanation:

Step 1:  Determine 0.47 as a fraction

0.47 can also be expressed as 47% which means that there is 47/100.  We can see that there is no way that we can simplify the fraction even more so that is our final answer.

Step 2:  Determine -0.47 as a fraction

0.47 can also be expressed as -47/100.  We can see that there is no way that we can simplify the fraction even more so that is our final answer.

Step 3:  Determine --0.47 as a fraction

Two negatives (-), means that they cancel out and cause a positive (+).  For example, -1 * -1 gives us 1.  Therefore it would just be like the first one which is 47/100.

Answer: Part (a) = 47/100, Part (b) = -47/100, Part (c) = 47/100

Please help me with my math homework

Answers

 

n this world, no one can survive alone. Team up with friends to fend off countless waves of zombies, fight bosses, earn coins, level up, and buy new towers! If you're feeling up for a challenge, try taking on harder bosses on harder difficulties!

Consider parallelogram VWXY below.
Use the information given in the figure to find m∠YXV, m∠Y, and x.

Answers

Answer:

56°, 84°, 3 units

Step-by-step explanation:

Properties of a parallelogram

Two adjacent angles are supplementaryOpposite angles are congruentOpposite sides are parallel and congruent

Use the properties to find the required parameters

1) Find m∠YXV

m∠YXV + m∠VXW + m∠VWX = 180°m∠YXV + 40° + 84° = 180°m∠YXV = 180° - 124°m∠YXV = 56°

2) Find m∠Y

m∠Y = m∠W = 84°

3) Find x

2x = 6x = 6/2x = 3

Answer:

m∠YXV = 56°

m∠Y = 84°

x = 3

Step-by-step explanation:

Sum of interior angles of a triangle = 180°

⇒ m∠W + m∠WVX + m∠VXW = 180°

⇒ 84° + m∠WVX + 40° = 180°

⇒ m∠WVX = 56°

As VW ║ YX  and  YV ║ XW  then  m∠WVX = m∠YXV

So m∠YXV = 56°

In a parallelogram, opposite angles are congruent

⇒ m∠Y = m∠W

m∠Y = 84°

In a parallelogram, opposite sides lengths are congruent

⇒ VW = YX

⇒ 2x = 6

⇒ x = 6 ÷ 2

x = 3

There are 8 teams to play against each other in a tournament. How many ways can 1st and 2nd place be awarded at the end of the tournament?

Answers

Answer:

28

Step-by-step explanation:

Correct option is C)

Matches played between 8 teams =7+6+5+4+3+2+1=21

The number of ways that can 1st and 2nd place be awarded at the end of tournament is 56.

What is permutation?

A permutation is an arrangement of objects in a definite order. The members of elements of sets are arranged here in a sequence where order matters.

According to the given question

we have  to find,

Number of ways  for 1st and 2nd place can be awarded

Number of ways for 1st place be awarded  = 8

Number of ways for 2nd place be awarded = 7

Therefore,

The total number of ways can 1st and 2nd place be awarded = (8)×(7)

=56.

Learn more about permutation here:

https://brainly.com/question/2295036

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What is the equation of the line that is perpendicular two and has the same y-intercept as the line with (0,1) and (5,0)

Answers

Answer:

its all about reletives so if u take the number then multiply by five u get 56.3

Step-by-step explanation:

u know

4) Calculate the exact circumference of OP
5 cm
P
12 cm

Answers

12 + 5 = P + 360° - (90° x 2)

17 = 360°P - 180°

17 = 180° => P = 180° - 90° = 90° => P - 5 = P + (5 + 12) => P = 14 in <90 5 CM Angle, P = 14 - 1 = 13 without offset

13

Answer:

40.84

Step-by-step explanation:

5cm^2 +25cm^2=169

sqaure root of 169 =13

13= diameter

6.5= radius

2 pie r = circumference

6.5x2 pie = 40.84

What is the approximate surface area of the figure? Use 3.14 for pi. 65.72 cm² 113.04 cm² 37.68 cm² 75.36 cm²

Answers

113.04 cm²

==========

The figure given is a sphere with a radius of 3 cm

formula for surface area of sphere : 4πr²

Solve:

⇒ 4πr²

⇒ 4(3.14)(3)²

⇒ 113.04 cm²

113.04 cm²

Solving it:

The SA given is 4πr²

To get your answer

First, you multiply these

4πr²

Add/ Plug-in the radius:

4(3.14)(3)²

And this is your answer:

113.04 cm²

I have attached an image showing this is the correct answer!

please help me if you can tysm! :))))​

Answers

9.9 is your final answer

Answer:

9.9

Is the answer to the question

8th grade mathe help8th grademath heelp

Answers

Answer:So for number 35 you will put the qwestion in a calculator... now you have your answer so put that ansor to the side, and solve all of the ones in the answer choices and see which one has a common answer from the one in the problem

Step-by-step explanation:

Which fractions are equivalent to 1 2 ? Select all that apply. A. 2 4 B. 3 6 C. 3 4 D. 4 8

Answers

Answer:

A , B And D


2/4 divide both numbers by to and you get 1/2


3/6 divide both numbers by 3 and you get 1/2


4/8 divide both numbers by 4 and you get 1/2

Answer:
A
B
D
Step-by-step explanation:

12+12=24
12+12+12=36
12+12+12+12=48

Calculate the side lengths of the given scale.

Answers

Answer:

x: 4metres

y: 8metres

Step-by-step explanation:

using scale 1:4

x:16 ÷ 4

y: 2×4

The perimeter of a rectangle is $98,$ and the length of one of its diagonals is $41.$ Find the area of the rectangle.

Answers

Answer:

[tex]328units^2[/tex]

Step-by-step explanation:

First off,  I do want to say that you could word this more easily.

98 is the perimeter. length is 41. width is 8.

the area is length*width for rectangles.

98-41=57

57-41=16

16/2=8

8*41=328 units^2

Find the volume of a hemisphere that has the radius of 3 m to the nearest 10
(PLEASE ANSWER)

Answers

Volume of a hemisphere is 2/3•pi•r^3
The answer is 56.5m^3

Determine whether each set of data represents a linear, an exponential, or a quadratic function.

Answers

Answer:

See below ↓↓↓↓

Step-by-step explanation:

Set 1

[tex]\left[\begin{array}{ccc}x&y\\1&13\\2&6\\3&1\\4&-2\\5&-3\end{array}\right][/tex]

Quadratic [As it reduces at an unusual rate : -7, -5, -3, etc.]

Set 2

[tex]\left[\begin{array}{ccc}x&y\\-5&-34\\-4&-29\\-3&-24\\-2&-19\\-1&-14\end{array}\right][/tex]

⇒ y = 5x - 9

Linear

Set 3

[tex]\left[\begin{array}{ccc}x&y\\-2&0.0625\\-1&0.25\\0&1\\1&4\\2&16\end{array}\right][/tex]

Exponential [As seen by the perfect squares 0.0625, 0.25, 1, 4, 9..]

Set 4

[tex]\left[\begin{array}{ccc}x&y\\-6&28\\-3&19\\-1&13\\0&10\\3&1\end{array}\right][/tex]

Quadratic [As it reduces at an unusual rate : -9, -6, -3, etc.]

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