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Math Help - why does ∫c dz/(1 + z^4) = 2πi [(-1/4) e^(πi/4) + (-1/4) e^(3πi/4)] = π/√2.

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    why does ∫c dz/(1 + z^4) = 2πi [(-1/4) e^(πi/4) + (-1/4) e^(3πi/4)] = π/√2.

    why does ∫c dz/(1 + z^4) = 2πi [(-1/4) e^(πi/4) + (-1/4) e^(3πi/4)] = π/√2.

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    Re: why does ∫c dz/(1 + z^4) = 2πi [(-1/4) e^(πi/4) + (-1/4) e^(3πi/4)] = π/√2.

    What is the countour you are integrating?
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    Re: why does ∫c dz/(1 + z^4) = 2πi [(-1/4) e^(πi/4) + (-1/4) e^(3πi/4)] = π/√2.

    C represents

    counterclockwise-oriented contour C consisting of the upper half circle of radius R centered at the origin ( γ) and the real axis for x in [-R, R].
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    Re: why does ∫c dz/(1 + z^4) = 2πi [(-1/4) e^(πi/4) + (-1/4) e^(3πi/4)] = π/√2.

    Quote Originally Posted by blueyellow View Post
    C represents

    counterclockwise-oriented contour C consisting of the upper half circle of radius R centered at the origin ( γ) and the real axis for x in [-R, R].
    Why don't you use partial fractions decomposition and then just use the residue theorem, or Cauchy's integral formulat, etc.?
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