Help me: Solve: z^4 = -4

All answers should be in the format a+bi where a and b are real numbers

Answers

Answer 1

z²-2i=0

Answer:

Solution given:

z⁴=-4

doing square root on both side

[tex]\sqrt{z⁴}=\sqrt{2²*-1}[/tex]

we know i²=-1

substituting i² we get

z²=[tex]\sqrt{2²*i²}[/tex]

z²=2i

z²-2i=0 is a required answer. where

z² and 2 is real number.

Answer 2

Answer:

  z = {-1 -i, -1 +i, 1 -i, 1 +i}

Step-by-step explanation:

Using Euler's formula, we can write the equation as ...

  z^4 = 4e^(i(π +2πn)) . . . . . . where n is any integer

Then the 4th root is ...

  z = (√2)e^(i(π +2πn)/4 = (√2)e^(i(π/4 +nπ/2)) . . . . . for n = 0–3

  z = √2(cos(π/4+nπ/2) +i·sin(π/4 +nπ/2)) . . . . . for n = 0–3

  z = ±1 ±i

  z = {1 +i, -1 +i, -1 -i, 1 -i}

_____

Additional comment

Values of n are only needed in the range 0–3, because the answers repeat for values other than those.


Related Questions

In your own words, describe how to find the GCF for a set of numbers. Use the numbers 24 and 32 as an example. (PLS HELP ILL GIVE 50 points and brainlest also no links please, thanks)

Answers

Answer:

8

Step-by-step explanation:

We can find GCF by prime factorising

24 = 2³ × 3

32 = 2⁵

Common factor = 2³ = 8

Hence,

GCF of 24 and 32 is 8.

Hope it helps

Which of the following triangles shows a centroid?

Answers

Answer:

first option

Step-by-step explanation:

30 POINTS! "A triangle with the side lengths of these numbers CAN exist: 9, 3, and ____?

Answers

Answer:

Let the third side be x

We know that

Sum of two sides of a triangle must be greater than the third side

So,

9 + 3 > x

12 > x (1)

Also, difference of two side of triangle must be smaller than the third side

9 - 3 < x

6 < x (2)

From 1 and 2 we concluded

6 < x < 12

The length of third side would lie between 7 to 11

Find the slope of the graphed line.

ASAP​

Answers

y = mx+b

y = 1/3x+4

Sincerely,

William

How do u solve this

Answers

2 should be the answer

Whats 12 3/8 - 9 1/8

Answers

Answer:

3[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Answer:

13/4

Step-by-step explanation:1238−918

Convert 1238

to an improper fraction.

Tap for more steps...

998−918

Convert 918

to an improper fraction.

Tap for more steps...

998−738

Combine the numerators over the common denominator.

99−738

Subtract 73

from 99

.

268

Cancel the common factor of 26

and 8

.

Tap for more steps...

134

Interpreting Composite Functions in the Real World
Try it
The volume of air in a balloon is represented by the function von = = nr?, where r is the radius of the balloon, in
inches. The radius of the balloon increases with time, in seconds, by the function rt) = 42
Write a composite function that can be used to determine the volume of the balloon after t seconds. Then, select the
two true statements

Answers

Answer:

Answer is A and C on edge

Step-by-step explanation:

The composite function that can be used to determine the volume of the balloon after t seconds, when V is composed with r is 1/48πt⁶ and after 6 second it is 972π.

What is composite function?

When the two or more than two functions are written in the form of single function. Then such function is called the composite function.

Let suppose there is a function f(x) and another function g(x). Then the composite function can be given as,

[tex]f[g(x)][/tex]

The volume of air in a balloon is represented by the function,

[tex]V(r)=\dfrac{4}{3}\pi r^3[/tex]

Here, r is the radius of the balloon, in inches.

The radius of the balloon increases with time, in seconds, by the function,

[tex]r(t) = \dfrac{1}{4}t^2[/tex]

The composite function that can be used to determine the volume of the balloon after t seconds is,

[tex]V(r(t))=\dfrac{4}{3}\pi (\dfrac{1}{4}t^2)^3\\V(r(t))=\dfrac{4}{3}\pi (\dfrac{1}{64}t^6)\\V(r(t))=\dfrac{1}{48}\pi t^6[/tex]

After the 6 seconds,

[tex]V(r(6))=\dfrac{1}{48}\pi (6)^6\\V(r(6))=\dfrac{1}{48}\pi \times46656\\V(r(6))=972\pi[/tex]

Thus, the composite function that can be used to determine the volume of the balloon after t seconds, when V is composed with r is 1/48πt⁶ and after 6 second it is 972π.

Learn more about the composite function here;

https://brainly.com/question/10687170

#SPJ2

What are the domain and range of each relation?
Drag the answer into the box to match each relation.

Answers

Answer:i cant see it that well its blurry

Step-by-step explanation:

Answer:

The domain of the graph is {-3, -1, 1, 4}. The range of the graph is {-4, -1, 1, 4}

The domain of the set of ordered pairs is {-4, -3, 1}. The range of the set of ordered pairs is {1, 3, 4}

Step-by-step explanation:

I need help with this to

Answers

Answer:

-7 , 9

1, -3

5, -9

Step-by-step explanation:

Answer:

The answer is

-7 , 9, 1, -3, 5, -9

Hope this helps;)

༒Question༒


refer to attachment


nonsense will get report​

Answers

Answer:

REFER TO ATTACHEMENT

I HOPE IT IS HELPFUL

Solve using elimination.

y = 3x + 4
3y = 3x + 8

Answers

Answer:

4y=9x+12

Step-by-step explanation:

the answer should be that's it


In a scale drawing, 3 millimeters represents 17 meters. Exactly how many millimeters represents 55 meters?

Answers

Answer:

See image

Step-by-step explanation:

Compare "like" values to write a proportion (two fractions or ratios set equal to each other) Then you can cross multiply to solve the equation for x

is (-a + b)² = a² - 2ab + b² right or wrong, and why?

Answers

Answer:

[tex]\huge\boxed{\sf Right.}[/tex]

Step-by-step explanation:

[tex](-a+b)^2[/tex]

Let's apply the formula (x+y)² = x² + 2xy + y²

Here, x = -a and y = b

So,

= (-a)² + 2(-a)(b) + (b)²

= a² - 2ab + b²

Hence, it has been proved that (-a + b)² = a² - 2ab + b².

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807

The area of the shaded region is 20 cm. Find the value of x

Answers

if you could put more info ab this then i would understand what u want me to put

if f(x) = 2x^ 2 + 3x,then what is f(−9)?

Answers

Answer:

f(-9) = 135

Step-by-step explanation:

Replace x with -9, and evaluate the expression.

f(x) = 2x² + 3x

f(-9) = 2(-9)² + 3(-9)

f(-9) = 2(81) - 27

f(-9) = 162 - 27

f(-9) = 135

(-1, 16), (-13, 6)

Write an equation in slope-intercept form.

help

Answers

Answer:

y=5/6x+101/6

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(6-16)/(-13-(-1))

m=-10/(-13+1)

m=-10/-12

simplify

m=5/6

y-y1=m(x-x1)

y-16=5/6(x-(-1))

y-16=5/6(x+1)

y-16=5/6x+5/6

y=5/6x+5/6+16

y=5/6x+5/6+96/6

y=5/6x+101/6

PLEASE HELP WHAT IS THE DOMAIN AND RANGE OF THIS GRAPH

Answers

Pay attention in school bud

2) A gym charges a $30 membership fee and $10 per month. Write an
equation to represent this situation. Find the cost for 5 months. If a new
member paid $160, how many months did they go to the gym?

Answers

C = 10m + 30, where C is total cost and m is # of months

C = 10(5) + 30

C = 50 + 30

C = $80

$160 = 10m + 30

160 - 30 = 10m

130/10 = m

m = 13 months

Hope that helps

Eva spent $11.61 downloading songs, and each song cost $1.29. Four students wrote and solved equations to find s, the number of songs that she downloaded. Which student wrote and solved the equation correctly?
Seba’s work:
1 dollar and 29 cents = 11 dollars and 61 cents. S = 10.
Ari’s work:
1 dollar and 29 cents = 11 dollars and 61 cents. S = 9.
Erick’s work:
StartFraction s Over 1 dollar and 29 cents EndFraction = 11 dollars and 61 cents. S = 14.98.
Daniel’s work:
StartFraction s Over 1 dollar and 29 cents EndFraction = 11 dollars and 61 cents. S = 9.

Answers

Answer:

1.29s = 11.61

s = 9

Step-by-step explanation:

1.29s = 11.61

s = 11.61/1.29

s = 9

Answer:

The correct answer is Ari's work

Step-by-step explanation:

right on edge

Welcome!^^

Find the future value of an annuity due of $7,000 paid at the beginning of each 6-month period for 8 years if the interest rate is 8%, compounded semiannually. (Round your answer to the nearest cent.)

Answers

Answer: Im not sure but i think its 120,960

Step-by-step explanation: i know that there is 2 of the 6-month periods in a year and multiplied that by 8 and got 16. Then i did 7000x.08=560 and then i added that to 7000 and got 7560. FInally i multiplied that by 16 and got 120,960.

can someone help me with this answer plsss

Answers

Answer: 44 ft

Step-by-step explanation:

if you add up the right square it adds up to 16 4+4+4+4 all sides are equal since its a square.

The left rectangle is

8+8=16

6+6=12

16+12=28

Now you add the square on the right to the square on the left which is

28+16= 44 ft

Chef Ira has 613 pies he wants to sell at his restaurant. Each slice is 16 pie and costs $1.50. Chef Ira sells all the remaining slices of pie.


How much money will he earn?


A. $9.00

B. $9.50

C. $38.00

D. $57.00

Answers

D is the answer see picture attached

-8.5x +0.43 = -2.97
The solution is x =

Answers

Answer:

x=0.4

Step-by-step explanation:

ubtract

0.43

from both sides of the equation.

8.5

x

=

2.97

0.43

Subtract

0.43

from

2.97

.

8.5

x

=

3.4

Divide each term in

8.5

x

=

3.4

by

8.5

.

8.5

x

8.5

=

3.4

8.5

Divide

3.4

by

8.5

.

x

=

0.4

someone help me please

Answers

Answer:

54m^2

Step-by-step explanation:

Area for a triangle = 1/2(12*9)

12 x 9 = 108

108/2 = 54

54m^2 have a good day

please help this is due tomorrow and im having a lot of trouble figuring these out

Answers

Ok done. Thank to me :>

Which of the following is a government retirement program that offers a tax incentive?
A. Roth IRA
B. Opt- out program
C. A 529 plan
D. Contribution matching

Answers

the correct answer is B!

Find the slope of the line that passes through (-10, -52) and (56, -37).

Answers

15/66 I think you might be able to simplify

hope you get it
{2x−y=4
y−x=4

Answers

Step-by-step explanation:

System of Linear Equations entered :

[1] 2x-y=4 [2] y-x=4

Equations Simplified or Rearranged :

  [1] 2x - y = 4   [2] -x + y = 4

Graphic Representation of the Equations :

y + 2x = 4 y - x = 4

Solve by Substitution :

// Solve equation [2] for the variable  y 

 

[2] y = x + 4

// Plug this in for variable  y  in equation [1]

  [1] 2x - (x +4) = 4   [1] x = 8

// Solve equation [1] for the variable  x 

  [1] x = 8 

// By now we know this much :

  x = 8   y = x+4

// Use the  x  value to solve for  y 

  y = (8)+4 = 12 

Solution :

 {x,y} = {8,12} 

Como se faz o cálculo 13÷5,2

Answers

a resposta para a sua pergunta é 2.5 esperança que ajuda por favor marcar como mais inteligente se correto obrigado

PLS HELP ME ASAP
DO NOT use any links

Answers

Answer:

c

Step-by-step explanation:

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