Recent content by Measle

  1. Measle

    Undergrad Confused by the behavior of sqrt(z^2+1)

    I see - how does that lead to -it and it? or rather how do you find the discontinuities of sqrt(1 + z^2)?
  2. Measle

    Complex Analysis - sqrt(z^2 + 1) function behavior

    Homework Statement Homework Equations The relevant equation is that sqrt(z) = e^(1/2 log z) and the principal branch is from (-pi, pi] The Attempt at a Solution The solution is provided, since this isn't a homework problem (I was told to post it here anyway). I don't understand why the...
  3. Measle

    Undergrad Confused by the behavior of sqrt(z^2+1)

    (mentor note: this is a homework problem with a solution that the OP would like to understand better) In Taylor's Complex Variables, Example 1.4.10 Can someone help me understand this? I don't know what they mean by (i, i inf), or how they got it and -it
  4. Measle

    Undergrad Principal branch of the log function

    I'm learning complex analysis right now, and I'm reading from Joseph Taylor's Complex Variables. On Theorem 1.4.8, it says "If a log is the branch of the log function determined by an interval I, then log agrees with the ordinary natural log function on the positive real numbers if and only if...