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3 years ago

If (3-4i) (x+iy) = 3 root 5 show that x^2 + y^2=9/5

Mathematics

1 answer:

NNADVOKAT [17]3 years ago

5 0

Answer:

the answer is 2 + i.

Step-by-step explanation:

Let the square root of 3 + 4i be x + iy.

So (x + iy) (x +iy) = 3 +4i

=> x^2 + xyi + xyi + i^2*y^2 = 3 + 4i

=> x^2 – y^2 + 2xyi = 3 + 4i

Equate the real and complex terms

=> x^2 - y^2 = 3 and 2xy = 4

2xy = 4

=> xy = 2

=> x = 2/y

Substitute in

=> x^2 - y^2 = 3

=> 4/y^2 - y^2 = 3

=> 4 – y^4 = 3y^2

=> y^4 + 3y^2 – 4 = 0

=> y^4 + 4y^2 – y^2 – 4 =0

=> y^2(y^2 + 4) – 1(y^2 + 4) =0

=> (y^2 – 1) (y^2 + 4) =0

Therefore y^2 = 1, we ignore y^2 = -4 as it gives complex values of y.

Therefore y = 1 and x = 2/1 = 2

The required square root of 3 + 4i is 2 + i.

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Hey I am super confused about the equation below. plzz help!!!

marshall27 [118]

Answer:

50.

Step-by-step explanation:

12 x 45 = 540. 45 + 5 = 50.

5 0

2 years ago

Can I have help with the question

sleet_krkn [62]

Answer:

Midpoint = (3.5, 4.5)

Perpendicular bisector = y = $\frac{7}{9}$ x + $\frac{16}{9}$

Step-by-step explanation:

[] We can solve this using the midpoint formula:

-> See attached

[] Plug-in our coordinates and solve:

$(\frac{7+0}{2} ,\frac{0+9}{2} )=(\frac{7}{2} ,\frac{9}{2} )=(3.5,4.5 )$

[] Now we will find the slope to solve for the perpendicular bisector.

-> We will use slope-intercept form, see attached

$\frac{9-0}{0-7}=\frac{9}{-7}$

-> The slopes of two perpendicular lines are negative reciprocals of each other, so $\frac{7}{9}$ will be the slope of or perpendicular bisector

-> Now we can solve for the equation by using y – y1 = m ( x – x1), were y1 and x1 are the coordinates of our midpoint

y - 4.5 = $\frac{7}{9}$ (x-3.5)

y - 4.5 = $\frac{7}{9}$ x- $\frac{49}{18}$

y = $\frac{7}{9}$ x- $\frac{49}{18}$ + 4.5

y = $\frac{7}{9}$ x + $\frac{16}{9}$

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

6 0

2 years ago

What is a verbal expression for w-24

schepotkina [342]

Question: What is a verbal expression for w-24

Answer: What is a 24 less than a number <em>w.</em>

Explanation: It would be (What is a 24 less than a number <em>w.</em>), because less than means subtract and you will write it the opposite of how you say it.

Hope It Helps!!

5 0

3 years ago

Slove for y show all your work 12y + 4 = 8y-12

Vedmedyk [2.9K]

Answer:

y = -4

Step-by-step explanation:

12y + 4 = 8y-12

Subtract 8y from each side

12y - 8y +4 = -12

4y +4 = -12

Subtract 4 from each side

4y +4-4 = -12 -4

4y = -16

Divide by 4

4y/4 = -16/4

y = -4

8 0

3 years ago

Read 2 more answers

First line joins ordered pairs negative 4, 3 and 2, negative 3. Second line joins negative 4, negative 3 and 2, 3. Part A shaded

elena55 [62]

The part that represents the solution to the inequality will be Part B shaded below first line and above second line.

<h3>How to depict the inequality?</h3>

From the information given, the equation of the first line will be:

y - 3 = (-3 - 3/2 + 4)(x + 4)

y - 3 = -1(x + 4)

y + x = -4 + 3

x + y = -1

The equation of the second line will be:

y + 3 = -1(x + 4)

y = x + 4 - 3

y = x + 1

This is plotted on the graph attached.

From the systems of equations, the statement that is correct about the two systems of equations is that They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 3 times the second equation of System A.

Learn more about inequalities on:

brainly.com/question/12215820

#SPJ1

4 0

2 years ago