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Complex mapping

  1. Jul 31, 2009 #1
    For f(z) = z^2 find the image of x + y = 1

    f(z) = z^2 = (x + iy)^2 = x^2 + 2ixy - y^2

    u(x,y) = x^2 - y^2
    v(x,y) = 2xy
     
  2. jcsd
  3. Jul 31, 2009 #2

    Mark44

    Staff: Mentor

    Here's how I would approach this problem. Every point on the line has coordinates (in the complex plane) of (x, 1 - x). A point on this line can be represented as z = x + i(1 - x). What does your function f do to these complex numbers?
     
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