1) Write the sum or difference in the standard form a + bi. (2 points)
( 7 + 5i) - ( -9 + i)

a) 16+4i
b) -16-4i
c) 16-4i
d) -2+6i

2) Write the product in standard form. (2 points)
( 7 + 7i)( 6 + 7i)

a) -7 + 91i
b) 49i2 + 91i + 42
c) 91 - 7i
d) -7 - 91i

3) Find the product of the complex number and its conjugate. (2 points)
1 + 3i

a) 1 + 9i
b) 10
c) -8
d) 1-9i

4) Write the expression in standard form. (2 points)
three divided by quantity three minus twelve i.

a) - one divided by seventeen. + four divided by seventeen. i
b) one divided by seventeen. - four divided by seventeen. i
c) - one divided by seventeen. - four divided by seventeen. i
d) one divided by seventeen. + four divided by seventeen. i

5) Find the real numbers x and y that make the equation true. (2 points)
5 + yi = x + 3i

Answers

Answer 1
When performing addition and multiplication with constant numbers, we treat i as we would treat any variable x in an expression, with the same rules and properties of addition and multiplication.

1)

[tex]( 7 + 5i) - ( -9 + i)=7+5i+9-i=(7+9)+(5i-i)=16+4i[/tex]

2)
Distribute 7+7i over 6 and 7i:

[tex]( 7 + 7i)( 6 + 7i)=( 7 + 7i)\cdot6+( 7 + 7i)\cdot7i=42+42i+49i+49i^2[/tex]

collecting similar terms, and substituting [tex]i^2[/tex] with -1 we have:

42+91i-49=-7+91 i

3)

The conjugate of a complex number a+bi is a-bi;
the conjugate of 1+3i is 1-3i.

Thus, using the difference of squares formula we have

[tex](1+3i)(1-3i)=1^2-(3i)^2=1-9i^2=1-9(-1)=1+9=10[/tex]

4)

To write a rational expression ( with a complex number in the denominator) in the standard form, we multiply by the conjugate of the denominator both the numerator and the denominator:

[tex]\displaystyle{ \frac{3}{3-12i}= \frac{3(3+12i)}{(3-12i)(3+12i)}= \frac{9+36i}{3^2-(12i)^2} [/tex]

[tex]=\displaystyle{ \frac{9+36i}{9+144}= \frac{9+36i}{153}= \frac{9}{153}+ \frac{36}{153}i [/tex]


simplifying by 9, the complex number is finally written as 

[tex]\displaystyle{ \frac{1}{17}+ \frac{4}{17}i [/tex]


5)

2 complex numbers a+bi, and c+di are equal only if a=c, and b=d. (Where a, b, c, d are real numbers.)

Thus, x=5, and y=3 is the solution to the equation.


Answers:

1) A
2) A
3) B
4) D
5) (x, y) =( 5, 3)

Related Questions

I conceived on september 27 when will the test show the results

Answers

There isn't an exact time it's whenever they figure it out

Find two numbers whose sum is 49 and whose product is 544

Answers

17 and 32
I know this because,
17+32=49
And,
17×32=544

The two numbers are 16 and 33. They satisfy the conditions that their sum is 49 and their product is 544, as verified by setting up and solving a system of equations.

To find two numbers whose sum is 49 and whose product is 544, we can set up a system of equations based on the information given. Let's call the two numbers x and y. So, we have two equations:

x + y = 49xy = 544

By solving these equations simultaneously, we can find the values of x and y.

The easiest way to solve this might be to express y in terms of x from the first equation: y = 49 - x. Then, substitute this into the second equation:

x(49 - x) = 544

This simplifies to a quadratic equation:

x^2 - 49x + 544 = 0

Factoring this quadratic equation, we get:

(x - 16)(x - 33) = 0

Which gives us two possible values for x:

x = 16x = 33

Plugging these back into the equation for y, we get:

y = 49 - 16 = 33y = 49 - 33 = 16

So the two numbers are 16 and 33.

A rancher needs to enclose two adjacent rectangular​ corrals, one for cattle and one for sheep. if the river forms one side of the corrals and 180 yd of fencing is​ available, find the largest total area that can be enclosed.

Answers

Refer to the diagram shown below.

x = the width of each rectangular fence
y = the length of each rectangular fence

The amount of fencing available is 180 yards, therefore
2x + 2y = 180
x + y = 90               (1)

The total fenced area is
A = 2xy                 (2)

From (1), obtain
y = 90 -x               (3)
Substitute (3) into (2).
A = 2x(90 - x) = 180x - 2x²

To maximize A,
A'(x) = 180 - 4x = 0   => x = 180/4 = 45 yds
y = 90 -x = 45 yds

The largest total enclosed area is
A = 2*x*y = 2*45² = 4050 yd²

Answer: 4050 yd²

a rectangle is three centimeters.longer than it is wide. if its length were to be decreased by two centimeters, its area would decrease by thirty square centimeters.
A) what are the dimensions?
B) what is it’s area?
Show your work using an equation

Answers

given/equations formed from text:
I: l=w+3
II: A=l*w
III: new area B=(l-2)*w
IV: B=A-30

substitute l in II with I to remove l:
II': A=l*w=
(w+3)*w=
w^2+3w

substitute l in III with I to remove l:
III': B=(l-2)*w=
(w+3-2)*w=
(w+1)*w=
w^2+w

substitute A and B from II' and III' into IV:
B=A-30
w^2+w=w^2+3w-30
30=2w
w=15

insert w=15 into I:
l=15+3=18
->
A) dimensions of full size rectangle are width 15 and length 18
dimensions of reduced size rectangle are width 15 and length 16

B) full size: 15*18=10*18+5*18=180+90=270cm^2
reduced size: 15*16=10*16+5*16=160+80=240cm^2


What is the value of the function at x=−3?



y = 4

y = 3

y = 0

y=−3

Answers

It looks like y = 4.  Why is the graph black?
You just move to that x value on the x axis then go to your graph (line) and what y - value is it across from?

Answer:

y=4

Step-by-step explanation:

What time is 3 hours and 30 minutes before 5:00 P.M.?

Answers

5 - 3 = 2

2 pm so far

2:00 - 0:30 = 1:30 pm

your answer is 1:30 pm

hope this helps
1:30p.m is the time it would be

6​-ounce bag of rice noodles makes 5 servings. at that​ rate, find how many ounces of noodles are needed for 88 ​servings, to the nearest ounce

Answers

6 / 5 = 1.2 oz per serving <== ur unit rate

for 88 servings :
88 * 1.2 = 105.6....105 oz of noodles are needed <==

If molly walks 4 miles in 70 minutes, then molly will walk how far in 100 minutes if she walks at the same speed the whole time? if necessary, round your answer to the nearest tenth of a mile.

Answers

Find out how far Molly walks in 1 minute.

4/70 = 0.057 miles
In 100 minutes,
0.057x100 = 5.714 miles

Rounded to the nearest tenth, 5.7 miles.

Hope I helped :)

On Call 3.5 hours: $10 Talk Time 1/2 hours: $1.25 What is the unit rate in dollars per hour for each company?

Answers

On Call's unit rate is about $2.86 per hour, since $10/3.5 hours= $2.86/1 hour
Talk Time's unit rate is about $2.50 per hour, since $1.25/0.5 hours= $2.50/1 hour

Which of the following is the contrapositive of the conditional below?

If 3 + 4 = 6, then 2 · 5 = 10.

A. If 2 · 5 = 10, then 3 + 4 = 6.
B. If 3 + 4 ≠ 6, then 2 · 5 ≠ 10.
C. If 2 · 5 ≠ 10, then 3 + 4 ≠ 6.
D. If 3 + 4 ≠ 6, then 2 · 5 = 10.

Answers

Answer: If 2 · 5 ≠ 10, then 3 + 4 ≠ 6.


Step-by-step explanation:

Because a contrapositive is the contradiction the hypothesis and conclusion of something given and interchanging them. For example: "if not-B then not-A " is the contrapositive of "if A then B "

Answer:

If 2 · 5 ≠ 10, then 3 + 4 ≠ 6.

Step-by-step explanation: Hope This Helps You!!! :)))

Janine has two important tests to study for. If she plans to divide her study time equally between both tests, how long should she spend studying for each test if she wants to study for at most 90 minutes?

Answers

90/2 = 45
45 minutes each.

90 mins divide by 2 tests = 45 mins per test

a person mailing postcards earns a fixed amount for each postcard he mails yesterday his hourly wage was $14 an hour if he worked 5 hours yesterday and mailed 300 postcards how much does he earn for each postcard mailed? show you work

Answers

If he worked 5 hours and his rate is $14/hr, then he earned a total of $70.
He mailed 300 postcard, so each postcard mailed is $0.2333..

BTW, i actually think the question is incomplete, so this may actually be a wrong answer.

For each postcard person gets $14/60 or $0.2333.

What is ratio?

Ratio is basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, there ratio will be a:b .

Given that,

Wage for 1 hour = $14,

Since,

The person mailed 300 postcards in 5 hours,

therefore, in 1 hour 60 postcards will be mailed.

Person gets $14 for 60 postcards ,

So for 1 postcard person will get $14/60 or $0.2333 .

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in a simple random sample of 48 men, the mean wrist circumference of the men is 19.3 centimeters with a standard deviation of 1.2 centimeters. Round your answer to the nearest hundredth.

Which interval is the 95% confidence interval for the mean wrist circumference for all men?

18.99,19.61
18.96, 19.64
12.85, 19.75
19.14, 19.46

Answers

Answer: Choice B
The 95% confidence interval for the population mean mu is (18.96, 19.64)
--------------------------------------------------------------
--------------------------------------------------------------

Work Shown:

xbar = 19.3
s = 1.2
n = 48
z = 1.960 (use a calculator or table to compute this critical value)

Lower Limit L
L = xbar - z*(s/sqrt(n))
L = 19.3 - 1.960*(1.2/sqrt(48))
L = 18.9605180417166
L = 18.96

Upper Limit U
U = xbar + z*(s/sqrt(n))
U = 19.3 + 1.960*(1.2/sqrt(48))
U = 19.6394819582836
U = 19.64

The confidence interval is therefore (L,U) = (18.96, 19.64)

Final answer:

The 95% confidence interval for the mean wrist circumference for all men is 18.91 to 19.69 centimeters.

Explanation:

To calculate the confidence interval for the mean wrist circumference, we can use the formula: CI = x ± t(s/√n), where CI is the confidence interval, x is the sample mean, t is the t-value corresponding to the desired confidence level, s is the sample standard deviation, and n is the sample size.

In this case, the sample mean is 19.3 centimeters, the sample standard deviation is 1.2 centimeters, and the sample size is 48. We can find the t-value for a 95% confidence level using a t-table or calculator. Assuming a normal distribution, the t-value is approximately 1.96. Plugging in these values into the formula, we get:

CI = 19.3 ± 1.96(1.2/√48) = 19.3 ± 0.3956

Therefore, the 95% confidence interval for the mean wrist circumference is approximately 18.91 to 19.69 centimeters.

Sales fall from 300 per week to 270 per week what’s the percentage change

Answers

Hi there! 

Your question: 

Sales fall from 300 per week to 270 per week what's the percentage change?

My answer:

The formula for calculating percent change is as follows: 

[(y2 - y1)/y1]*100=your percent change 

y2= first value 
y1=second value 

Plug the numbers in: 

[(300-270)/300]*100

[30/300]*100

0.1*100

10 

Therefore, the percent change is 10%

Hope this helps! Let me know if it's incorrect so I can fix it:)

Evaluate the expression below when x = 5.

3x(2x - 7)

A.) 0
B.) 24
C.) 45
D.) 143

Answers

the answer is D 143. welcome

Identify the Asymptotes for the graphs below help pls!

Answers

Asymptotes are lines that continues to approach a given curve but never actually meets it! For the second figure it is the Y axis since the curves slowly appear to approach the Y axis! Not sure about the first figure(probably the X axis)!
Asymptotes are lines that continues to approach a given curve but never actually meets it! For the second figure it is the Y axis since the curves slowly appear to approach the Y axis! Not sure about the first figure(probably the X axis)!

If (a+b)^2=25, and a^2+b^2=17, then what is a*b equal to? Thanks.

Answers

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

substituting:-

17 = 25 - 2 a*b
a*b =  (25-17) / 2 =  8/2 =  4 answer


If 5kg more than 3 times mac’s mass is decreased by twice his mass the result is 60 kg. What is mac’s mass?

Answers

Let x be mac's mass 

(3x+5)-(2x)=60 
3x+5-2x=60 
x=60-5 
x=55 

Therefore, Mac is 55 kg 

Hope I helped :)

Mac's mass can be found by setting up the equation 3m + 5kg - 2m = 60kg, simplifying to m + 5kg = 60kg, and solving for m to get m = 55kg. Therefore, Mac's mass is 55kg.

The equation, according to the problem statement, is: 3m + 5kg - 2m = 60kg. This simplifies to m + 5kg = 60kg, from which we can subtract 5kg from both sides resulting in m = 55kg. So, Mac's mass is 55kg.

Steps to solve the problem:

Let m represent Mac's mass.

Write the equation according to the problem statement: 3m + 5kg - 2m = 60kg.

Simplify the equation: m + 5kg = 60kg.

Subtract 5kg from both sides: m = 55kg.

Conclude that Mac's mass is 55kg.

A line contains the points (34, 12)(34, 12) and (32, 48)(32, 48) .

What is the slope of the line in simplified form?

Answers

the slope of the line in simplified form is -18.
The answer to this question is -18

Rearrange the formula v = GM r for r.

Answers

The correct formula for [tex]\( r \)[/tex] rearranged from [tex]\( v = \frac{GM}{r} \) is \( r = \frac{GM}{v} \)[/tex].

To rearrange the formula [tex]\( v = \frac{GM}{r} \)[/tex] to solve for [tex]\( r \)[/tex], follow these steps:

1. Start with the given formula:

[tex]\[ v = \frac{GM}{r} \][/tex]

2. Multiply both sides of the equation by [tex]\( r \)[/tex] to get rid of the denominator:

[tex]\[ vr = GM \][/tex]

3. Divide both sides of the equation by [tex]\( v \)[/tex] to isolate [tex]\( r \)[/tex]:

[tex]\[ r = \frac{GM}{v} \][/tex]

This gives us the rearranged formula for [tex]\( r \)[/tex] in terms of [tex]\( G \), \( M \), and \( v \)[/tex]

What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?

15.3 units
20.4 units
30.6 units
52.0 units

Answers

To calculate the perimeter, consider each side separately. Since this is a rectangle, you have 2 pairs of sides of equal length, so you just have to calculate the length of one of each pair of sides and then double each and add them to find the perimeter.

Top side: If you look carefully, this side is really the hypotenuse of a triangle that is 2 units tall and 10 units long. Using the Pythagorean Theorem, you can calculate the length of the hypotenuse to be 2^2 + 10^2 = c^2 --> c = 10.2

Left side: Just like the top side, this side is the hypotenuse of a triangle that is 5 units tall and 1 unit long. Pythagoras again: 5^2 + 1^2 = c^2 --> c = 5.1

Since you have two of each side that are the same length, double each and add for the final perimeter: 10.2*2 + 5.1*2 = 30.6
firstly, we will name the points as the following:
(-6,4)  will be named as A
(4,2) will be named as B
(3,-3) will be named as C 
(-7,-1) will be named as D 
then we will use the distance formula between any 2 points on the graph which equals=[tex] \sqrt({x}1-{x}2)^2 +({y}1-{y}2)^2[/tex]
So,
AB=[tex] \sqrt[/tex](-6-4)^2+(4-2)^2 =2[tex] \sqrt[/tex]26
BC=[tex] \sqrt[/tex](4-3)^2+(2+3)^2 = [tex] \sqrt[/tex]26
CD=[tex] \sqrt[/tex](3=7)^2+(-3+1)^2 = 2[tex] \sqrt[/tex]26
AD=[tex] \sqrt[/tex](-6+7)^2+(4+1)^2 =[tex] \sqrt[/tex]26
Now calculate the sum and it will equal=30.6

What proportion of a normal distribution corresponds to z scores greater than 1.04?

Answers

Final answer:

The proportion of a normal distribution for z scores greater than 1.04 is 0.1492, which is found by subtracting the area to the left (0.8508) from the total area under the curve (1).

Explanation:

To find the proportion of a normal distribution that corresponds to z scores greater than 1.04, we must look up the area to the left of the z-score using a z-table or a standard normal distribution table. Once we have the area to the left, we can calculate the area to the right by subtracting this value from 1 (since the total area under the curve is 1). For a z-score of 1.04, the z-table shows that the area to the left is approximately 0.8508. Therefore, the proportion that is greater than a z-score of 1.04 is 1 - 0.8508, which equals 0.1492.

The standard normal distribution (Z~N(0,1)) has a total area of 1 under the curve, and it is symmetric about the mean, which is 0. Z-scores give us a way to determine how many standard deviations an observation is from the mean. Additionally, common z-scores used to determine confidence intervals or the proportion of observations within a certain range are tied to the percentage areas under the curve. For example, a z-score of ±1 encompasses approximately 68% of the data, ±2 about 95%, and ±3 approximately 99.7%.

Write a 10 digit number such that the first digit tells how many zeros

Answers

1234567890 or 2134567800 or 3000216789

Ria is an Indian student who was admitted to a US university. Her annual tuition is $42,000. She has to pay her tuition fees in US dollars. She needs to calculate how many Indian rupees she will need to buy one dollar. The dollar to rupee exchange rate is 63.76 and rupee to dollar exchange rate is 0.015. How many Indian rupees will Ria need to buy one dollar?

50.00 rupees

56.00 rupees

63.76 rupees

76.63 rupees

Answers

1$ = 63.76 rupees (dollar to rupee exchange)
1 rupee = 0.015$ (rupee to dollar exchange)
To buy one dollar, Ria will need 63.76$
Answer: (c)

Now, Ria's annual fees is $42,000. To know how much this is in dollars, use cross multiplication as follows:
tuition fees = (42,000*63.76) / (1) =  2,677,920 rupees

Ria will need 2677920 Rupees to pay her tuition fees

Data;

Tuition fee = $42,000$1 = 63.76 rupees$1 rupees = $0.015

How Many Rupees will she need to buy a Dollar?

We need to convert the currency from dollars to rupees

From the data given in the question, $1 is equivalent to 63.7 Rupees.

This information can further be used to determine how many Rupees she needs to pay her Tuition fees.

[tex]\$1 = 63.76 Rupees\\\$42,000 = x\\x = 42000 * 63.76\\x = 2677920[/tex]

Ria will need 2677920 Rupees to pay her tuition fees

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How to determine the probability of an event with a small chance repeating?

Answers

OOH USE YOUR BRAiN AND THINK :D

If 3 (x+1) =7 find the value of 3x

Answers

The value of 3x would be 4/3.
Distribute the 3 in the parenthesis and you get:
3x+3=7
Then subtract 1 on both sides of the equal side.
3x=4
Therefore, the value of 3x would be 4.

the probability that it will rain today is 0.3 what is the probability that it will not rain?

Answers

Okay. 0.3 means that there is 30% chance that it will rain today. Subtract that number from 100 to get the chance it won’t rain. 100 - 30 = 70. There is a 70% chance that it will not rain today.

Answer: 0.7

Step-by-step explanation: 1-0.3 = 0.7

What is the first step in solving an equation by completing the square?

Answers

Write the quadratic in the correct form, it must be in descending order and equal to zero.

A polynomial function P(x) has a degree n. If n is even is the number of turning points of the graph of p(x) even or odd? What can you say about the number of turning points if n is odd?

Answers

I think the number of turning points if n is even  is odd.
For n = odd it could be odd or even.

The number of turning points if n is odd if A polynomial function P(x) has a degree n, is even.

What is polynomial?

A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and positive-integer powers of variables. It is made up of indeterminate (also known as variables) and coefficients.

Given:

A polynomial function P(x) has a degree n,

A turning point is when the derivative's sign changes. A relative maximum or relative minimum might mark a turning point (also known as local minimum and maximum). A turning point is a stationary point if the function is differentiable, however not all stationary points are turning points.

For example, if the degree is 2 then the number of turning points will be 1

The general formula is, the number of turning points = n - 1

Thus, for odd n, the turning point will be even.

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"in how many ways can 6 people be lined up to get on a bus?"

Answers

36, just do 6 times 6
The answer would be 6! 
Putting it another way it could also be
6*5*4*3*2*1= 720 ways.
So there would be 720 ways 6 people can be lined up on a bus.
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