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Troyanec [42]
3 years ago
6

Find the distance using the modulus of the difference between z1 = -8 + 3i and z2 = 7 - 4i. Show all work for full credit.

Mathematics
2 answers:
3241004551 [841]3 years ago
5 0

Answer:

\sqrt{274}

Step-by-step explanation:

Given z_1=-8+3i,\ z_2=7-4i.

1. Find the difference z_1-z_2:

z=z_1-z_2=-8+3i-(7-4i)=-8+3i-7+4i=(-8-7)+(3i+4i)=-15+7i.

This complex number has real part Rez=-15 and imaginary part Imz=7.

2. The modulus of complex number z is

|z|=\sqrt{Re^2z+Im^2z}=\sqrt{(-15)^2+7^2}=\sqrt{225+49}=\sqrt{274}.

Sindrei [870]3 years ago
3 0
<h2>Answer:</h2>

The distance between z_1\ \text{and}\ z_2 is:

                        16.5529 units

<h2>Step-by-step explanation:</h2>

We know that the difference between two complex numbers:

z_1=a_1+ib_1\ \text{and}\ z_2=a_2+ib_2 is given by:

|z_1-z_2|=|(a_1+ib_1)-(a_2+ib_2)|\\\\i.e.\\\\|z_1-z_2|=|(a_1-a_2)+i(b_1-b_2)|\\\\|z_1-z_2|=\sqrt{(a_1-a_2)^2+(b_1-b_2)^2}

Here we have:

z_1=-8+3i\ \text{and}\ z_2=7-4i

i.e.

a_1=-8\ ,\ b_1=3,\ a_2=7\ \text{and}\ b_2=-4

i.e. we have:

|z_1-z_2|=\sqrt{(-8-7)^2+(3-(-4))^2}\\\\|z_1-z_2|=\sqrt{15^2+7^2}\\\\|z_1-z_2|=\sqrt{225+49}\\\\|z_1-z_2|=\sqrt{274}\\\\|z_1-z_2|=16.5529

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Answer:

480.53 yards

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<h3>How to determine the cosine ratio?</h3>

The complete question is added as an attachment


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h^2 = 25 + 144

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The cosine ratio is then calculated as:

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This gives

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Klio2033 [76]

Given that cost of 1 drinks in a glass bottle = $2.00

Given that cost of 1 drinks in an aluminum can = $0.50

Given that cost of 1 drinks in a plastic bottle = $1.50

Then sum of costs  of 1 drink from each will be = 2.00+0.50+1.50


Given that you buy two of each then total cost will be given by 2(2.00+0.50+1.50)


Hence expression that represents the amount of money you will spend is 2(2.00+0.50+1.50).

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2(2.00+0.50+1.50)=2*2.00+2*0.50+2*1.50

This is final answer of part A.


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Given that refund on 1 drinks in a glass bottle = $0.05

Given that refund on 1 drinks in an aluminum can = $0.10

Given that refund on 1 drinks in a plastic bottle = $0.15

Then sum of refunds on 1 drink from each will be = 0.05+0.10+0.15


Given that you plan to recycle all of the items you purchased then total refund will be given by 2(0.05+0.10+0.15)


Hence expression to represent the amount of refund you will receive is 2(0.05+0.10+0.15).

Using distributive property, we can rewrite it as:

2(0.05+0.10+0.15)=2*0.05+2*0.10+2*0.15

This is final answer of part B.


----------

Net cost is given by difference of total cost and total refund

Net cost = 2(2.00+0.50+1.50) - 2(0.05+0.10+0.15)

= 2*2.00+2*0.50+2*1.50 - (2*0.05+2*0.10+2*0.15)

= 4+1+3 - (0.10+0.20+0.30)

= 8 - 0.60

= 7.40

Hence net cost is $7.40

5 0
3 years ago
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