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3 years ago

What is the product of 4+3i and 4-3i

2 answers:

8 0

So we know that i=the square root of -1 so
we multiply and notice that is is in the format of the differnece of two perfect squares which is (x)^2-(y)^2=(x-y)(x+y) so
we notice that 4=x and 3i=y so

(4-3i)(4+3i)=(4)^2-(3i)^2

(3 times the square root of -3)^2=(9 times -1)=-9
4^2 is 16
16-(-9)=subtracting a negative=adding a positive so =16+9=25
the answer is 25

mash [69]3 years ago

7 0

Use the formula $(a+b)(a-b)=a^2-b^2$ .

$(4+3i)(4-3i)=4^2-(3i)^2=16-9i^2 \\ \\
i^2=-1 \\ \\
16-9i^2=16-9 \times (-1)=16+9=25 \\ \\
\boxed{(4+3i)(4-3i)=25}$

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The three vertices of a triangle drawn on a complex plane are represented by 0 + 0i, 4 + 0i, and 0+ 3i. The length of the hypote

EastWind [94]

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The area is base*half height = 4*3/2 = 6.

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3 years ago

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2 years ago

Alondra received a 14% hourly raise, but the number of hours worked decreased by 7.5%. If her wage was $10.50 an hour and she wo

Elodia [21]

Answer:

She will earn $442.89 in one week after the changes.

And this is more than her previous weekly earnings.

Step-by-step explanation:

Given:

Alondra received a 14% hourly raise, but the number of hours worked decreased by 7.5%. If her wage was $10.50 an hour and she worked 40 hours per week before the changes.

Now, to find money she will earn in one week after the changes.

Her wage was = $10.50.

She worked per week = 40 hours.

So, her salary before changes:

$10.50\times 40\\\\=\$420.$

Thus, the salary per week before changes is $420.

Now, to get her salary after 14% hourly raise:

$10.50+14\%\ of\ 10.50\\\\=10.50+\frac{14}{100} \times 10.50\\\\=10.50+1.47\\\\=11.97$

Salary after hourly raise = $11.97 per hour.

Then, to get the number of hours worked decreased by 7.5%:

$40-7.5\%\ of\ 40\\\\=40-\frac{7.5}{100} \times 40\\\\=40-3\\\\=37.$

Number of hours per week after hours of worked decreased = 37 hours.

Now, to get the salary after changes:

Salary after hourly raise × number of hours per week after hours of worked decreased

$=11.97\times 37$

$=\$442.89.$

Salary after changes in one week = $442.89.

As, the previous salary was $420 in one week. 

And after changes this salary is $442.89 in one week which is more than previous. 

Therefore, she will earn $442.89 in one week after the changes.

And this is more than her previous weekly earnings.

4 0

3 years ago

The area of a rectangle is 5454 in squaredin2. the ratio of the length to the width is 3 : 23:2. find the length and the width.

MrRa [10]

hello :
let : x the length and y the width
the area is : xy and ; x/y = 3/2
xy =5454 ...(1)
x = (3/2)y ... (2)
subsct in (1) : (3/2)y ×y = 5454
3y² = 10908
y² = 3636....continue calculate : y

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3 years ago

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2 years ago

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