Turn on thread page Beta
    • Thread Starter
    Offline

    14
    ReputationRep:
    I'm given that f_1(x+iy) = u_1(x,y)+iv_1(x,y) and f_1 is differentiable everywhere on the complex plane.

    Given that u_1(x,y) = 2x^2 - 2xy - 2y^2 and f_1(1) = 2, I'm supposed to find f_1(z).

    I found v_1(x,y) = 4xy - y^2 using the Cauchy Riemann equations.

    So f_1(z) = u_1(x,y) + iv_1(x,y) = 2x^2 - 2xy - 2y^2 + 4xyi - y^2 i

    Which is really annoying to simplify!

    I've gotten to the point where

    f_1(z) = 2(x+iy)^2 -y^2i -2xy and now I'm stuck.
    • Study Helper
    Offline

    15
    Study Helper
    (Original post by wanderlust.xx)
    I've gotten to the point where

    f_1(z) = 2(x+iy)^2 -y^2i -2xy and now I'm stuck.
    What about using z+\bar{z}=2x etc. as a basis for building the trailing parts of that formula.
    Offline

    2
    ReputationRep:
    You have the wrong eqn for v1(x,y)

    When using the Cauchy-Riemann eqns, you will be doing partial integration which means you should have a function of integration rather than a constant of integration to include in your eqn for v1(x,y).

    It then becomes simple to simplify!

    BTW, are you sure that f1(1) = 2 and not f1(1) = 2+i, ?
 
 
 
Poll
Is the Big Bang theory correct?
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.