How would I simplify these expressions? (Pre-Calculus) I know that you are supposed to multiply all of these to do so, but every time I do that, I still get the wrong answer. My textbook says that these are the answers:
19: -15 + 8i
21: 8 + 6i
23: 34
25: 85
Could anyone explain how they got these answers? Mine are way off. Is the book just wrong? In #21, how would 3 times 3 equal 8 in the answer? Am I missing something?
Since you have the answers, I'll just show the steps on how to get there.
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Problem 19
[tex](1+4i)^2\\\\(1+4i)(1+4i)\\\\1*1 + 1*4i + 4i*1 + 4i*4i\\\\1 + 4i + 4i + 16i^2\\\\1 + 4i + 4i + 16(-1)\\\\1 + 4i + 4i-16\\\\(1-16) + (4i+4i)\\\\(1-16) + (4+4)i\\\\-15 + 8i\\\\[/tex]
Keep in mind that [tex]i = \sqrt{-1}[/tex] by definition. Squaring both sides leads to [tex]i^2 = -1[/tex]
In the second step, I used the idea that x^2 = x*x. Right after that, I used the FOIL rule to expand everything out.
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Problem 21
We could follow the same idea as problem 19, but I'll use a different approach.
[tex](A+B)^2 = A^2+2AB+B^2\\\\(3+i)^2 = 3^2 + 2*3*i + i^2\\\\(3+i)^2 = 9 + 6i - 1\\\\(3+i)^2 = 8 + 6i\\\\[/tex]
The formula on the first line is the perfect square binomial formula.
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Problem 23
The FOIL rule can be used if you want, but I'll use the difference of squares rule instead.
[tex](m+n)(m-n) = m^2 - n^2\\\\(3+5i)(3-5i) = (3)^2 - (5i)^2\\\\(3+5i)(3-5i) = 9 - 25i^2\\\\(3+5i)(3-5i) = 9 - 25(-1)\\\\(3+5i)(3-5i) = 9 + 25\\\\(3+5i)(3-5i) = 34\\\\[/tex]
It turns out that multiplying any complex number of the form a+bi with its conjugate a-bi will result in a purely real number (that has no imaginary part). More specifically: [tex](a+bi)(a-bi) = a^2+b^2[/tex]
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Problem 25
We could use the difference of squares rule again, but I'll show a different approach. This time using the distribution rule. The FOIL rule could also be used if you wanted.
[tex](6+7i)(6-7i)\\\\x(6-7i)\\\\6x-7xi\\\\6(x)-7i(x)\\\\6(6+7i)-7i(6+7i)\\\\6(6)+6(7i)-7i(6)-7i(7i)\\\\36+42i-42i-49i^2\\\\36-49(-1)\\\\36+49\\\\85\\\\[/tex]
I used x = 6+7i and the substitution property to help distribute. Lines 3 and 6 are where distribution is applied.
Write the prime factorization of 26.
Answer:
The factors of 26 are 1,2,13,26 The prime factors of 26 are 2 and 13.
Step-by-step explanation:
Answer:
2 and 13
Step-by-step explanation:
First, we can see that the last digit of
26
is even, and thus
26
is divisible by
2
. If we divide by
2
, we find
26
2
=
13
. As
13
is a prime number, there are no further prime factors of
26
, and so the prime factorization of
26
is
2
×
13
.
can anyone solve this step by step for me
Answer:
0.5 ㏑ | 1-2x | +c
Step-by-step explanation:
Formula: ∫ 1/ax+b dx = 1/a ln Iax+bI +c
The combined amount of ingredients are sugar, brown and white 8 cups, write an addition equation to solve how many cups of brown sugar was added if the chef used 4 cups of sugar
Answer: Yo MAMA + Yo nasty daddy = them having a mistake which is you lol
Step-by-step explanation:
Select the interval where h(x)< 0.
Choose 1 answer:
(А) -3.5
(в) -2 < x < -1
(C) 2.5
Answer:
Step-by-step explanation:
C
Which steps show how to use the distributive property to evaluate 5 * 58?
Answer:
B.
Step-by-step explanation:
When using the distributive property, you distribute the leading number to each number inside the parentheses.
Answer:
Option B is correct.
Step-by-step explanation:
The answer of Option B is correct. 58 × 5 = 290.
Therefore, Option B is correct.
help please
i will give the best one
There are 56 fourth graders going on a field trip. The teacher wants to divide them evenly into groups of 4 students and no more than 8 students. What are ways to divide the students evenly into groups
56 ÷14 =4
Step-by-step explanation:
dividing
56÷7=8
please help me with this sum I will mark you as brainest
Answer:
2016÷6=336 336×6=2016
3186÷9=354 354×9=3186
give a try for next sums
1. Tim's phone service charges $27.42 plus an additional $0.18 for each text message sent per
month. If Tim's phone bill was $31.92, how many text messages did he send that months
Answer:
25 text messages
Step-by-step explanation:
First of all you need to find how much money was added to his phone bill. 31.92-27.42 would equal 4.5. Then you would divide that number by 0.18 to find out the total text messages, which is 25
Write an equation in point-slope form of the line that passes through the point (4,−9) and has a slope of 6.
The equation is y−
Answer:
Step-by-step explanation:
Okay, so the point-slope form is
(y - y1) = m(x - x1)
Where m = the slope of the line
and where (x1, y1) is a point on the line
So, if the slope is 6, then m = 6
Now, you plug that and the point (4, -9) into the equation above.
(y -(-9)) = 6(x - 4)
y + 9 = 6(x - 4)
This is the point slope form of the line
Circles C and C′ are similar. State the translation rule and the scale factor of dilation.
Question 12 options:
A) To obtain C′, circle C is translated to the right four units and down three units and is dilated with a scale factor of one.
B) To obtain C′, circle C is translated to the left three units and up two units and is dilated with a scale factor of 1∕2.
C) To obtain C′, circle C is translated to the right three units and down two units and is dilated with a scale factor of one.
D) To obtain C′, circle C is translated to the right three units and down two units and is dilated with a scale factor of two.
an investment had return of 13% if inflation was 4.1% what was your real return ?
Answer: 8.9%
Step-by-step explanation: 13 - 4.1
A long-sleeve shirt has 8 front buttons and 2 cuff buttons; a short-sleeve shirt has 6 front buttons and no cuff buttons. The factory which makes ‘Slimboy Shirts’ uses 10 times as many front buttons as cuff buttons. What is the ratio of long-sleeve shirts to short-sleeve shirts produced by the factory?
Leave your ratio in its simplest form.
Answer:
ratio of long-sleeved shirts to short-sleeved shirts is 1:2 this is my answer that I thought of if you don't feel comfortable believing me just wait for another person to answer and see what they say.
Step-by-step explanation:
Identify the measure of MN in the diagram.
See attachment picture please
Answer:
How can we answer it without question?
A vehicle purchased for $25000 depreciates at a constant rate of 5% per year. Determine the approximate value of the vehicle 12 years after purchase. Round to the nearest whole number.
Answer:
$13,509.
Step-by-step explanation:
After each year the vehicle is worth 95% of the previous value.
95% = 0.95.
So after 12 years the approximate value
= 25000 * 0.95^12
= $13,509.
Fluffy the bunny ate 1 4 of a carrot in the morning, and he ate some more at night. By the end of the day, he still had 1 3 of the carrot left to eat. How much of the carrot did Fluffy the bunny eat at night?
Answer:
She ate 5/12 of carrot hope it's help
Marsha Hansen, the manager of the Flint Plant of the Michigan Company is responsible for all of the plant's costs except her own salary. There are two operating departments within the plant, Departments A and B. Each department has its own manager. There is also a maintenance department that provides services equally to the two operating departments. The following information is available. (on the picture) Departments managers are responsible for the wages and supplies in their department. They are not responsible for their own salary. Building rents, utilities, and maintenance are allocated to each department based on square footage. Required: Complete the responsibility accounting performance reports below that list costs controllable by the manager of Department A, the manager of Department B, and the manager of the Flint plant.
I will post the template too
Part 1:
Answer:
Hello
Step-by-step explanation:
The graph below shows a distance versus time graph. What is the average speed
between 2 p.m. and 4 p.m.?
Answer Choices and Graph in the picture.
Answer:
option B is correct answer.
Step-by-step explanation:
(200-75)/2 = 62.5 miles per hour.
Identify the type of function graphed to the right.
o linear
exponential
other
As x increases by 1 unit, what is the exponential
growth factor?
9514 1404 393
Answer:
exponentialgrowth factor 3Step-by-step explanation:
If the function showed linear growth, it would be a straight line. Since it curves upward, it will be either "exponential" or "other." The growth factor seems more or less constant, so we can claim the curve to be exponential.
When x=1, y=1; when x=2, y=3. The increase in x by 1 unit causes the value to grow by a factor of 3/1 = 3. When x=3, y=9, which is growth by another factor of 3. The growth factor is 3.
Answer:
Am working on that too this is for everyone! here you go
Step-by-step explanation:
Edge 2021!
18 In the arithmetic sequence 4, 7, 10, 13, the ---BLANK--- is 3.
what is blank
Answer:
I don't understand
Step-by-step explanation:
Like How
Which of the functions represents a function?
Answer:
letter A or B but I think it's letter b
Answer:
The answer is A
Step-by-step explanation:
on edge 2021
Evaluate the expression
Answer:
7/12 or 0.583333333333...
Step-by-step explanation:
calculator
I think the answer is 0.83, tell me is it correct ok, I try to help you
What is the quotient of 15a4b3/12a2b ? Assume that the denominator does not equal zero.
Answer:
[tex]\frac{5a^2b^2}{4}[/tex]
Step-by-step explanation:
Which ones are true?
Answer:
The first, third and last one are true
Use the distributive property to write an expression equivalent to 7(48).
Drag and drop the appropriate number into each box.
Answer:
336
Step-by-step explanation:
7x48=
7(8)= 56
7(4)+5= 33
7(48) = 336
Answer:
336
Step-by-step explanation:
If g(x)=5|30x+4|, find g(2/3)
Answer:
Step-by-step explanation:
g(x)=5|30x+4|
g(2/3)=5|30×2/3+4|
=5|20+4|
=5×24
=120
can anyone help with this, please
Answer:
Step-by-step explanation:
As the zeros are x = -2 and x = 2, the factors are (x + 2) and (x - 2)
y = C(x + 2)(x - 2) = C(x² - 4)
applying the y intercept of (0, 4)
4 = C(0² - 4)
C = -1
y = -1(x² - 4)
y = 4 - x²
Answer:
hi
Step-by-step explanation:
The first term of an arithmetic sequence is 4. The rule a↓n=a↓n+1 + 5 can be used to find the next term of the sequence.
a 4
b 5
c 9
d -1
Answer:
c. 9
Step-by-step explanation:
Using the rule, substituting 4 for a↓1, we find the next term to be ...
[tex]a_2 = a_1 +5\\\\a_2=4 +5\\\\\boxed{a_2=9}[/tex]