Sailing

Discussion in 'Geometry and Trigonometry' started by nycmathguy, Feb 16, 2022.

1. nycmathguy

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Section 6.5

Can you set up parts (a) and (b) to try on my own this weekend? Thanks.

nycmathguy, Feb 16, 2022
2. MathLover1

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a.
each ship as complex # (ai+bj)

b.

MathLover1, Feb 16, 2022
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3. Country Boy

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Since you are not using any property specific to complex numbers, it seems a bit silly to think of the vertical axis as an "imaginary axis". It is simpler to think of this as just a Cartesian coordinate system so that A is at (3, 4) rather than "3+ 4i" and B is at (-5, 2) rather than -5+ 2i.

In either case, the distance between them is sqrt((3- (-5))^2+ (4- 2)^2)= sqrt(64+ 4)= sqrt(68)= 2sqrt(17).

Country Boy, Feb 16, 2022
4. MathLover1

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I agree that way is simpler, but problem states to use the vertical axis as an "imaginary axis"

MathLover1, Feb 16, 2022
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5. nycmathguy

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I will try to do both parts using your hints.

nycmathguy, Feb 16, 2022
6. nycmathguy

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Which way is simpler? Are you talking about Country Boy's suggestions?

nycmathguy, Feb 16, 2022
7. Country Boy

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Then just replace "(a, b)" with "a+ bi".

Country Boy, Feb 17, 2022
8. nycmathguy

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Ha!

nycmathguy, Feb 18, 2022
9. nycmathguy

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The book's answer for part (b) is as follows:

"Find the modulus of the difference of the complex numbers."

1. What's a modulus?

2. If my answer is wrong, why?

3. What does Ron Larson mean by his answer to part (b)?

nycmathguy, Feb 18, 2022
10. MathLover1

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1. the magnitude, it’s also called its length, or its absolute value
2. you need the difference of the complex numbers
3+4i-(-5+2i) =3+4i+5-2i=8+2i
To find modulus of a complex number z=a+bi we use formula:
|z|=sqrt(a^2+b^2)
you have a=8 and b=2
|z|=sqrt(8^2+2^2)=sqrt(68)=2sqrt(17)

MathLover1, Feb 18, 2022
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