(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:
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
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.
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.
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
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
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:
What is the slope of y =
-4?
Answers
Answer:
20
Step-by-step explanation:
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
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
Find m
70°
55°
80°
90°
Answers
Answer:
70°
Step-by-step explanation:
angle subtended by arc is half of arc
OKAY, guys give me a really brilliant explanation on how 2+2=4. It should be 22. It doesn't make sense.
Answers
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!~
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
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
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
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
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
x-y=3 what is this in slope intercept form
Answers
Answer:
y=x-3
Step-by-step explanation:
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
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
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
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.
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
f(n)=n-2 could some one please answer this?
Answers
Answer:
i dont know
Step-by-step explanation:
i dont know
I need help (20 points)
Answers
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
HELP PLEASE:(
Determine if the triangles are congruent by using HL?
Answers
Answer:
whats hl
Step-by-step explanation:
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
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
?
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