Turn on thread page Beta
    • Thread Starter
    Offline

    15
    ReputationRep:
    https://jacktilson.net/edu/maths/mar...ummer-2005.pdf
    If you go to page 26 , to question 7b! How do they get the final answer of u^2+v^2=1/2
    Ive done everything on top but i cant seem to get the final answer tbh?
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by English-help)
    https://jacktilson.net/edu/maths/mar...ummer-2005.pdf
    If you go to page 26 , to question 7b! How do they get the final answer of u^2+v^2=1/2
    Ive done everything on top but i cant seem to get the final answer tbh?
    Since they have the same denominator, you can add the fractions to get

    \displaystyle \frac{u^2+v^2}{\left(u^2+v^2 \right)^2} = 2

    Now try cancelling the fraction.
    • Thread Starter
    Offline

    15
    ReputationRep:
    (Original post by notnek)
    Since they have the same denominator, you can add the fractions to get

    \displaystyle \frac{u^2+v^2}{\left(u^2+v^2 \right)^2} = 2

    Now try cancelling the fraction.
    Ohhh yeahh , so simple , my brain :facepalm:
    • Thread Starter
    Offline

    15
    ReputationRep:
    Thank you , much appreciated
    Offline

    14
    ReputationRep:
    I don't do FM, so sorry if this is a stupid question, but why you do include the v's on the bottom when taking the real part and include the u's when taking the imaginary part?
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by h3rmit)
    I don't do FM, so sorry if this is a stupid question, but why you do include the v's on the bottom when taking the real part and include the u's when taking the imaginary part?
    Do you mean top? You may need to clarify what you mean.
    Offline

    14
    ReputationRep:
    (Original post by notnek)
    Do you mean top? You may need to clarify what you mean.
    On the second line, the v's are included in the bottom part (u^2 + v^2). But since they're the imaginary component , why are they included in the real part (and viceversa for the imaginary part and u's)
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by h3rmit)
    On the second line, the v's are included in the bottom part (u^2 + v^2). But since they're the imaginary component , why are they included in the real part (and viceversa for the imaginary part and u's)
    You don't do FM so I'm not sure what you know / don't know.

    Basically in the working they have reached this complex number:

    \displaystyle \frac{u-iv}{u^2+v^2}

    where u and v are real numbers. By splitting the fraction you can rewrite this:

    \displaystyle \frac{u}{u^2+v^2} - \frac{iv}{u^2+v^2} = \frac{u}{u^2+v^2}- \left(\frac{v}{u^2+v^2}\right)i

    So the real part of this complex number is \displaystyle \frac{u}{u^2+v^2} and the imaginary part is \displaystyle \frac{-v}{u^2+v^2}.
    Offline

    14
    ReputationRep:
    (Original post by notnek)
    You don't do FM so I'm not sure what you know / don't know.

    Basically in the working they have reached this complex number:

    \displaystyle \frac{u-iv}{u^2+v^2}

    where u and v are real numbers. By splitting the fraction you can rewrite this:

    \displaystyle \frac{u}{u^2+v^2} - \frac{iv}{u^2+v^2} = \frac{u}{u^2+v^2}- \left(\frac{v}{u^2+v^2}\right)i

    So the real part of this complex number is \displaystyle \frac{u}{u^2+v^2} and the imaginary part is \displaystyle \frac{-v}{u^2+v^2}.
    Ah, I was tforgetting v was a real number for some reason, never mind. Cheers
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: January 22, 2017
Poll
“Yanny” or “Laurel”
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.