(a + b)(a - b) = a^2 - b^2

1. Multiply the numerator and the denominator by the complex conjugate of the denominator.

2. Simplify the results into the real part and the imaginary part.

Divide the complex numbers. Show all work.

Answers

Answer 1

Answer:

Step-by-step explanation:

hello : given z = (-6-10i)/(4+7i)

the complex conjugate of the denominator is : 4-7i

1. Multiply the numerator and the denominator by the complex conjugate of the denominator: z = (-6-10i)(4-7i)/(4+7i)(4-7i)

use identity : (a + b)(a - b) = a² - b² calculate the product : (4+7i)(4-7i)

(4+7i)(4-7i) = 4² -(7i)² =16 -49i² =16+49 = 65..... ( i² = -1)

2) Simplify the results calculate the numerator : (-6-10i)(4-7i)

(-6-10i)(4-7i) = -24+42i -40i+70i² = -24+42i -40i-70 .....( i² = -1)

(-6-10i)(4-7i) = -94+2i

now : z = (-94+2i )/65 = (-94/65) +(2/65) i

the real part is : ( -94/65) and the imaginary part is : 2/65

Related Questions

The width of a rectangle is 1units less than the length. The area of the rectangle is 42 units

Answers

Answer:

Step-by-step explanation:

w=l-1

∵A=l×w

∴A=l×(l-1)

⇒42=l²-l

⇒l²-l-42=0 (After subtracting 42 from both sides)

Two factors of 42 that add to give negative 1 :-7+6

∴ (l-7)(l+6)=0

∴ l=7 or l=-6

but remember that length is a scalar quantity, hence l≠6 but l=7.

I hope this helped you solve this math problem and made you better understand

Write an equation in slope-intercept form of the line that passes through the given points.

Answers

i haven’t done this in a while but i believe it’s 1/3x-3

9 ( x - 5 ) = -108 solve for x

Answers

Answer:

x = -7

Step-by-step explanation:

9 ( x - 5 ) = -108

9x - 45 = -108

add 45 to each side of the equation:

9x = -63

divide both sides by 9:

x = -7

Answer:

x = - 7

Step-by-step explanation:

9(x - 5) = - 108

9x - 45 = - 108

9x - 45 + 45 = - 108 + 45

9x = - 63

9x ÷ 9 = - 63 ÷ 9

x = - 7

9. swimsuit: $22, 5% off, 4% tax

Answers

Answer:

21.74

Step-by-step explanation:

Are you looking for price of swimsuit including tax?

22 x .05 = 1.10 off

22-1.10=20.90 price before sales tax

20.90 x .04 = .84 tax on sales price

20.90 + .84 = 21.74 total paid

Find the volume of the cylinder. Use 3.14 for u. Round to the nearest whole number.
Radius-34 m
Height-45 m

Answers

Answer:

1530 cubic centimeters

A jar contains 4 green marbles 2 pink marbles 3 striped marbles. One marble is picked at random and then replaced. Then another marble is drawn at random again. What is the probability that both marbles are striped?

Answers

Answer:

25%

Step-by-step explanation:

Answer: It’s 1/9 I got the same question on my test.

The ratio of small dogs two big dogs at the park is 1: 3 which does not represent this ratio A. 3:9 B. 9:27 C. 2:4 D. 30:90

Answers

C(2.4) does not represent this ratio.

Answer:

2:4

Step-by-step explanation:

i did the test

NEED HELP FAST....Solve the following system of equations graphically. Select the graph that shows the correct solution of the system. 2x + y =3 3y = x - 12.... graph showing two lines intersecting at (3, 3) / graph showing two lines intersecting at (5, -7) / graph showing two lines intersecting at (3, -3) / graph showing two lines intersecting at (-3, -3)

Answers

Answer:

Step-by-step explanation:

Answer:

answer is c

Step-by-step explanation:

Anyone knows this? im giving 20 points pls answer , and it doesnt need to be big im just in 9th grade

Answers

Answer:

men=24%

women=72%

Step-by-step explanation:

100/250=0.4

0.4*180=72

0.4*60=24

i think this is the answer

A quality control manager samples 700 LED bulbs and finds defects in 8 of them. What is the probability that a bulb selected at random will have a defect?

Answers

Answer: 0.0114

Step-by-step explanation:

Since we are given the information that the quality control manager samples 700 LED bulbs and finds out that 8 bulbs have defects in them.

The probability that a bulb selected at random will have a defect will be calculated as follows:

= Number of defected bulbs / Total number of bulbs sampled

= 8/700

= 0.0114

Therefore, the probability is 0.0114.

OKAY, guys give me a really brilliant explanation on how 2+2=4. It should be 22. It doesn't make sense.

Answers

It 22 what are you talking about

Answer:

It does make perfect sense... Count with ya fingers and see 4 yourself.

Step-by-step explanation: Go back to kindergarten buddy...

~ thx 4 the points my dude!~

f(n)=n-2 could some one please answer this?

Answers

Answer:

i dont know

Step-by-step explanation:

i dont know

What is the slope of y =
-4?

Answers

Answer:

Step-by-step explanation:

PLEASE HELP ME i DONT KNOW how to do this!

Answers

Answer:

It's b

Step-by-step explanation:

It is b or the second option because -2 is equal or greater than A therefore it is option 2

Find m

70°
55°
80°
90°

Answers

Answer:

70°

Step-by-step explanation:

angle subtended by arc is half of arc

Explain how the mean, median, and mode affect your purchase decisions?

Answers

Answer:

When a frequency distribution is symmetric, the mean, median and mode coincide in their value (X = Me = Mo). ... In a distribution skewed to the right, the relationship is reversed, the mode is greater than the median, and this in turn is greater than the mean (Mo> Me>).

Step-by-step explanation:

l hope and this can help you

In a trapezoid, the length of one base is equal to its height and the length of the other base is twice its height. If the height is 10 centimeters, what is the area of the trapezoid?
Explain how you found your answer.
Enter the correct answers in the boxes.

Answers

Answer:

150cm²

Step-by-step explanation:

In a trapezoid, the length of one base is equal to its height and the length of the other base is twice its height. If the height is 10 centimeters, what is the area of the trapezoid?

The formula for the area of a trapezoid = 1/2(a + b) h

Where a = Length of the first base

b = Length of the second base

h= height of the trapezoid

h = 10cm

The length of one base is equal to its height

Hence:

a = h = 10cm

The length of the other base is twice its height.

b = 2h

h = 10cm

b = 10 × 2 = 20cm

Therefore, the Area of the Trapezoid =

1/2 (20 + 10)10

1/2 × 30 × 10

= 150cm²

HELP PLEASE:(
Determine if the triangles are congruent by using HL?

Answers

Answer:

whats hl

Step-by-step explanation:

x-y=3 what is this in slope intercept form

Answers

Answer:

y=x-3

Step-by-step explanation:

9
?
Find the arc length of the semicircle,
Either enter an exact answer in terms of ar or use 3.14 for 7 and enter your answer as a decimal.
units

Answers

Answer:

28.26 units

Step-by-step explanation:

Given:

Radius (r) = 9

π = 3.14

Required:

Arc length

Solution:

Arc length = θ/360 × 2πr

θ = 180° (half of a circle = 180°)

Plug in the values into the formula

Arc length = 180/360 × 2 × 3.14 × 9

Arc length = ½ × 56.52

Arc length = 28.26 units

determine the volume of rectangular prism 6cm 4m 4m

Answers

To determine the volume of a rectangular prism you multiple base*height*width which is going to be 6*4*4 so the volume is 96 m^3

Idil has a smart phone data plan that costs $25 per month that includes 10 GB of
data, but will charge an extra $20 per GB over the included amount. How much
would Idil have to pay in a month where she used 4 GB over the limit? How much
would Idil have to pay in a month where she used went over by x GB?

Answers

If you times 4 by 20 you would get 160 then you add the 25 per month and then you would get 185

Jayden has $0.56 worth of pennies and nickels. He has a total of 20 pennies and nickels altogether. Determine the number of pennies and the number of nickels that Jayden has.

There are ______ pennies and _______ nickels

Answers

Answer:

there are 7 nickels and 13 pennies

Claire had 4 1/6 feet of string. She used some string to hang out decorations. Now she has 1 5/6 feet of string left. How much string did claire use? Draw a model and solve.

Answers

Answer:

Length of string used by Claire = 7 / 3 feet

Step-by-step explanation:

Given:

Length of string Claire in starts = [tex]4\frac{1}{6}[/tex] feet

Length of string Claire in end = [tex]1\frac{5}{6}[/tex] feet

Find:

Length of string used by Claire

Computation:

Length of string Claire in starts = [tex]4\frac{1}{6}[/tex] feet = 25 / 6 feet

Length of string Claire in end = [tex]1\frac{5}{6}[/tex] feet = 11 / 6 feet

Length of string used by Claire = Length of string Claire in starts - Length of string Claire in end

Length of string used by Claire = [25 / 6] - [11 / 6]

BY taking LCM

Length of string used by Claire = [25 - 11] / 6

Length of string used by Claire = 14 / 6

Length of string used by Claire = 7 / 3 feet

Jamie wants to make an 80, or B, test average in her class. She scored 75 and 82 on her last 2 tests. What is the lowest grade she can make on her last test to finish with an 80 test average?

Answers

Answer:

Its probably too late now but the answer is 83

Step-by-step explanation:

83 is the lowest grade she can make on her last test to finish with an 80 test average.

What is Probability?

It is a branch of mathematics that deals with the occurrence of a random event.

Given that Jamie wants to make an 80, or B, test average in her class.

She scored 75 and 82 on her last 2 tests.

we need to find the lowest grade she can make on her last test to finish with an 80 test average

Let x be the e lowest grade she can make on her last test to finish with an 80 test average

75+82+x/3=80

157+x=240

Subtract 157 from both sides

x=83

Hence, 83 is the lowest grade she can make on her last test to finish with an 80 test average.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ2

In the system of equations
-3.0 - 4y = 4
-52 + y = 2
Is (2, 10) a solution to the system?

Answers

Answer:

No, (2, 10) is not a solution to the system

Step-by-step explanation:

The given set of equations are -

-3X - 4Y = 4 --- Eq(1)

-52X + Y = 2--- Eq (2)

Multiplying equation 2 by 4, we get

-3X - 4Y = 4 --- Eq(1)

4 *(-52X + Y = 2)--- Eq (2)

-3X - 4Y = 4 --- Eq(1)

-208X + 4Y = 8--- Eq (2)

Now we will add equation 1 and 2

-211 X = 12

X = 12/211

Hence, the given set of solution does not fit for the given two equations

Write an expression that represents the area of a circle with radius 3x^3. (For any circle with radius r, a=π r^2 = π .r .r ^.)

A. 9 π x ^9
B. 9π x6
C. 6π x9
D. 6π x^6

Answers

9514 1404 393

Answer:

B. 9πx^6

Step-by-step explanation:

Putting the given radius into the area formula gives ...

A = πr^2

A = π(3x^3)^2 = π(3^2)(x^(3·2))

A = 9πx^6

I need help (20 points)

Answers

since x = 3 is a line that goes from left to right and we need to find an equation that also goes left to right. we can do x = 5 or really any number to equal x to.

A point slope form a line that had a slope of 1/2 and goes through (-1,-3) is?

Answers

Answer:

y=1/2x-5/2

Step-by-step explanation:

y-y1=m(x-x1)

y-(-3)=1/2(x-(-1))

y+3=1/2(x+1)

y=1/2x+1/2-3

y=1/2x+1/2-6/2

y=1/2x-5/2

PLZ HELP

How many solutions does the equation 3s + 7 = 3 + 4 + 3s have? (5 points)

a
Two

b
None

c
One

d
Infinitely many

Answers

Answer:

(d) infinitely many solutions

Step-by-step explanation:

Subtract 3s from both sides of 3s + 7 = 3 + 4 + 3s. We get

7 = 3 + 4, or 7 = 7. This is always true. There are (d) infinitely many solutions.

Answer:

(d) infinitely many solutions.

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(a + b)(a - b) = a^2 - b^2 1. Multiply the numerator and the denominator by the complex conjugate of the denominator. 2. Simplify the results into the real part and the imaginary part. Divide the complex numbers. Show all work.

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(a + b)(a - b) = a^2 - b^2

1. Multiply the numerator and the denominator by the complex conjugate of the denominator.

2. Simplify the results into the real part and the imaginary part.

Divide the complex numbers. Show all work.