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Margaret [11]
3 years ago
13

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.

You might be interested in
A car is traveling at a constant speed of 60 miles per hour. How many feet does it travel in 10 seconds?
Nat2105 [25]

Answer:

880 ft.

Step-by-step explanation:

<em>First! We have to establish how many feet the car travels per hour. </em>

60 <em>(number of miles per hour)</em> x 5280 <em>(number of feet in a mile) </em>= 316,800 <em>(number of feet in an hour)</em>

<em>Next, since we know that there are 60 minutes in an hour we are going to divide our "number of feet in an hour" by 60 to get the "number of feet in a minute"</em>

316,800 ÷ 60 = 5280

<em>Once again, we are going to divide our "number of feet in a minute" by 60 to get the "number of feet per second".</em>

5280 ÷ 60 = 88

<em>Finally! We will multiple our "number of feet per second" by 10 to get how many feet the car can travel in 10 seconds.</em>

88 × 10 = 880

<em>So! Our car can travel 880 feet in 10 seconds.</em>

Hope this Helps! :)

<em>Have any questions? Ask below in the comments and I will try my best to answer.</em>

-SGO

<em> </em>

<em></em>

5 0
3 years ago
Can someone please help me for four and five I need to get it done in a few minutes please help
lakkis [162]
4.)6       2(6) + 4
   9        2(9)+ 4
   15      2(15) + 4
5 0
3 years ago
I need help!!! Parallel lines p and q are cut by two non parallel lines m and n as shown in the figure the value of x is degrees
S_A_V [24]

Answer:

x = 78° , y = 115°

Step-by-step explanation:

The angle adjacent to x on the left side is corresponding to 102° , then

x = 180° - 102° = 78°

----------------------------------------

y and 115° are corresponding angles and congruent, then

y = 115°

8 0
3 years ago
a chord of 12cm long of 8cm is away from the of the circle what is the lenght of the chord which is 6cm away from the centre
lana66690 [7]

Answer:

The length of the chord is 16 cm

Step-by-step explanation:

Mathematically, a line from the center of the circle to a chord divides the chord into 2 equal portions

From the first part of the question, we can get the radius of the circle

The radius form the hypotenuse, the two-portions of the chord (12/2 = 6 cm) and the distance from the center to the chord forms the other side of the triangle

Thus, by Pythagoras’ theorem; the square of the hypotenuse equals the sum of the squares of the two other sides

Thus,

r^2 = 8^2 + 6^2

r^2= 64 + 36

r^2 = 100

r = 10 cm

Now, we want to get a chord length which is 6 cm away from the circle center

let the half-portion that forms the right triangle be c

Using Pythagoras’ theorem;

10^2 = 6^2 + c^2

c^2 = 100-36

c^2 = 64

c = 8

The full

length of the chord is 2 * 8 = 16 cm

5 0
3 years ago
I need some help with this
lapo4ka [179]

Answer:

A. 1

Step-by-step explanation:

Since it's g(-4), we have to use the first option because that means that x is equal to less than -4.

3√x + 5

3 √-4 + 5

= 1

4 0
3 years ago
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