Sailing

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

  1. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    Section 6.5

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

    Screenshot_20220215-093619_Samsung Notes.jpg
     
    nycmathguy, Feb 16, 2022
    #1
  2. nycmathguy

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,989
    Likes Received:
    2,884
    a.
    each ship as complex # (ai+bj)

    b.
    upload_2022-2-15_22-31-16.jpeg
     
    MathLover1, Feb 16, 2022
    #2
    nycmathguy likes this.
  3. nycmathguy

    Country Boy

    Joined:
    Dec 15, 2021
    Messages:
    157
    Likes Received:
    38
    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
    #3
  4. nycmathguy

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,989
    Likes Received:
    2,884
    I agree that way is simpler, but problem states to use the vertical axis as an "imaginary axis"
     
    MathLover1, Feb 16, 2022
    #4
    nycmathguy likes this.
  5. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    I will try to do both parts using your hints.
     
    nycmathguy, Feb 16, 2022
    #5
  6. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    Which way is simpler? Are you talking about Country Boy's suggestions?
     
    nycmathguy, Feb 16, 2022
    #6
  7. nycmathguy

    Country Boy

    Joined:
    Dec 15, 2021
    Messages:
    157
    Likes Received:
    38
    Then just replace "(a, b)" with "a+ bi".
     
    Country Boy, Feb 17, 2022
    #7
  8. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    Ha!
     
    nycmathguy, Feb 18, 2022
    #8
  9. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    IMG_20220218_165541.jpg

    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
    #9
  10. nycmathguy

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,989
    Likes Received:
    2,884
    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
    #10
    nycmathguy likes this.
  11. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    At least I got the distance right.
     
    nycmathguy, Feb 19, 2022
    #11
Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.
Similar Threads
There are no similar threads yet.
Loading...