Turn on thread page Beta
    • Thread Starter
    Offline

    8
    ReputationRep:
    A transformation, T, maps the point P from the z plane to Q in the w plane, defined below.

     \displaystyle w = \frac{2-iz}{z}, z \in \mathbb{C}, z\neq 0

    a) What is the locus of the point P, if P is mapped to Q which has locus  arg(w)=\frac{ \pi }{3} .

    b) Find the Cartesian equation of the circle, that the arc that represents the locus of P lies on.

    c) Find the area bounded by the curve and the y axis.

    Could someone just have a go and tell me what answer they got so that I can see if I'm right.
    • Thread Starter
    Offline

    8
    ReputationRep:
    Anyone wanna have a go?
    Offline

    19
    ReputationRep:
    (Original post by Ano123)
    A transformation, T, maps the point P from the z plane to Q in the w plane, defined below.

     \displaystyle w = \frac{2-iz}{z}, z \in \mathbb{C}, z\neq 0

    a) What is the locus of the point P, if P is mapped to Q which has locus  arg(w)=\frac{ \pi }{3} .

    b) Find the Cartesian equation of the circle, that the arc that represents the locus of P lies on.

    c) Find the area bounded by the curve and the y axis.

    Could someone just have a go and tell me what answer they got so that I can see if I'm right.
    Is it the same as last night?
    Online

    20
    ReputationRep:
    circle with centre ( -√ 3, -1 ) and radius 2
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by TeeEm)
    Is it the same as last night?
    Yeah, just added the area bit on the end.
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by the bear)
    circle with centre ( -√ 3, -1 ) and radius 2
    And the area?
    Offline

    19
    ReputationRep:
    (Original post by Ano123)
    And the area?
    I will have it by the end of the evening as I have a very long to do list on my desk
    Online

    20
    ReputationRep:
    (Original post by Ano123)
    And the area?
    say please
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by the bear)
    say please
    I got  2\pi/3 -\sqrt3 .
    Online

    20
    ReputationRep:
    (Original post by Ano123)
    I got  4\pi/6 -\sqrt3 .
     4\pi/6 -\sqrt3
    Offline

    19
    ReputationRep:
    If I am going to write a solution I might as well steal it
    here is my version
    Name:  complex.jpg
Views: 34
Size:  29.8 KB
    Attached Images
      
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by the bear)
     4\pi/6 -\sqrt3
    How did you find the area?
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by TeeEm)
    If I am going to write a solution I might as well steal it
    here is my version
    Name:  complex.jpg
Views: 34
Size:  29.8 KB
    Slightly different to how I did it. I defined the arc using parametric equations (I have them in my thread yesterday) and then integrated with respect to t.
    Online

    20
    ReputationRep:
    (Original post by Ano123)
    How did you find the area?
    i counted the squares

    i sketched the circle. i noticed that the sector of which the y axis formed a chord had a 60 degree angle.
    i minused the triangles' area from the sector. job done
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: March 5, 2016

University open days

  1. University of Bradford
    University-wide Postgraduate
    Wed, 25 Jul '18
  2. University of Buckingham
    Psychology Taster Tutorial Undergraduate
    Wed, 25 Jul '18
  3. Bournemouth University
    Clearing Campus Visit Undergraduate
    Wed, 1 Aug '18
Poll
How are you feeling in the run-up to Results Day 2018?
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.