Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

hartnn

  • 6 months ago

f(z)=(x^3-3xy^2+2xy)+ i(3x^2 y-x^2+y^2-y^3) is analytic, find \(f^' (z)\) & f(z) in terms of z

  • This Question is Closed
  1. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(f'(z)\)

  2. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Milne Thompson Method ?

  3. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    w=(x^3-3xy^2+2xy)+ i(3x^2 y-x^2+y^2-y^3 ) what next ? would i find dw/dx or dw/dy ?

  4. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i had done similar problem, where i found dw/dx and then plugged in x= z, y= 0 will this work here ?

  5. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    because with that i am getting the complex term too, with the 'i' ...... and if i try x=0, y=z (can i do this ?) then i get f'(z) as z^2 -z^3 correct or not ?

  6. RyGuy
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    idek why i clicked on this. im am sooooo not smart enough for this lol.

  7. Miracrown
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Have you tried the partial derivatives ?

  8. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    dw/dx or dw/dy are partial derivatives only....

  9. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what next after i find dw/dx (or dw/dy) ?

  10. nipunmalhotra93
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    find partial derivative of f wrt x

  11. Miracrown
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 2

    right, we need to find both of those first

  12. Miracrown
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 2

    What would df/dx be ?

  13. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    f(z)=(x^3-3xy^2+2xy)+ i(3x^2 y-x^2+y^2-y^3) df/dx = (3x^2 -3y^2 +2y) + i (6xy -2x)

  14. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    df/dy = (-6xy +2x) + i(3x^2 +2y-3y^2)

  15. nipunmalhotra93
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    replace x by z-iy

  16. nipunmalhotra93
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and all the y terms will cancel out... leaving only z terms (as it is analytic)

  17. Miracrown
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 2

    df/dx is good :)

  18. nipunmalhotra93
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    do that in df/dx

  19. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i used milne thompson method for similar type of problem before...i would like to try same thing...

  20. Miracrown
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 2

    df/dy is good also

  21. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    basically i plugged in x=z and y=0 and things sorted out....in this problem, it doesn't..

  22. nipunmalhotra93
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Miracrown it is, but it'll make it a little more complicated. using f'(z)=df/dx is more straightforward,

  23. klimenkov
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    1 Attachment
  24. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so my final answer should be z^2 (z-i) ?

  25. Miracrown
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 2

    looks like for df/dy , the "i" component is minus

  26. nipunmalhotra93
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @hartnn I'm not really familiar with that method. But I think using the substitution x=z-iy in df/dx is fine too isn't it?

  27. Miracrown
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 2

    The document I am looking at for this method, writes x^3 - 3xy^2 + 2xy as u(x,y)

  28. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    "replace x by z-iy" what would df/dx convert to ??

  29. Miracrown
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 2

    3x^2 y - x^2 + y^2 - y^3 is written as v(x,y)

  30. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    share the doc please ?

  31. nipunmalhotra93
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    df/dx=3z^2-i2z

  32. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    wot? you can't just plug in that on right side only ? can u ?

  33. Miracrown
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 2

    df/dz = ux(x,y) + ivx(x,y) , where

  34. Miracrown
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 2

    ux is the partial derivative of u with respect to x and v is the partial derivative of v with respect to x

  35. nipunmalhotra93
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    See we know that df/dz=df/dx right? (the one on the right is a partial one) So, once you've found the one on the right (using partial differentiation, just replace x by z-iy as x+iy=z is already known)

  36. Miracrown
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 2

    then, vx(x,y) = - uy(x,y)

  37. nipunmalhotra93
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I just checked it the answer is f'(z)=df/dx=3z^2-i2z

  38. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    please wait

  39. Miracrown
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 2

    http://www.sciencedirect.com/science/article/pii/B9780080169392500214

  40. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i didn't know the answer, but after @klimenkov posted that screenshot, i tried plugging in x=z and y=0

  41. nipunmalhotra93
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @hartnn yea yea that'll work too...

  42. Miracrown
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so, basically, where we have df/dx , we input z for "x" and 0 for "y" , as you mentioned nd, that should work out .

  43. nipunmalhotra93
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @hartnn It's essentially the same thing I just made it more complicated lol sorry about that :P

  44. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry, my internet got disconnected.... did i do it correctly ?? or i integrated it one more time unnecessarily ???

    1 Attachment
  45. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i should get f(z) as z^2(z-i) right ?

  46. klimenkov
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Did you try to divide \(f(z)\) by \(x+ iy\) ?

  47. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thats dw/dx is same as f'(z) and after i integrate it i directly get f(z) right ?

  48. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    why would i do that division ?

  49. nipunmalhotra93
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @hartnn yes f(z)=z^3-i z^2.

  50. hartnn
    • 6 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Thanks all :) @klimenkov @nipunmalhotra93 @Miracrown

  51. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.