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Math Help - Quick check on an analytic function

  1. #1
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    Quick check on an analytic function

    This may seem stupid but...

    if  z = x + iy

    and i let U = x and V = y

     Ux= 1, Uy = 0 and  Vy = 1, Vx = 0

    can i say  Uy = -Vx ?

    i.e. the function f(z) = z is analytic
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  2. #2
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    Quote Originally Posted by Tekken View Post
    This may seem stupid but...

    if  z = x + iy

    and i let U = x and V = y

     Ux= 1, Uy = 0 and  Vy = 1, Vx = 0

    can i say  Uy = -Vx ?

    i.e. the function f(z) = z is analytic
    I assume you mean that U_x = 1, U_y = 0, V_x = 0, V_y = 1.

    Since U_x = V_y and U_y = -V_x, yes, the function is analytic.
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