Set a complex field exclude the origin and the real positive axis. Define z in the complex field 2, as zº = ealogn(z). F

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Set A Complex Field Exclude The Origin And The Real Positive Axis Define Z In The Complex Field 2 As Zo Ealogn Z F 1 (28.74 KiB) Viewed 38 times

Set a complex field exclude the origin and the real positive axis. Define z in the complex field 2, as zº = ealogn(z). For z = relo, loge(re) = log(r) + i0. Set a keyhole contour in 2, as the diagram below: 75m 18 Re Let a be a positive real number smaller than 1. Calculate the integration below by integrating over the keyhole contour. (with R goes to infinity, and both and 8 goes to zero) 1 So 2²(x + -dx = R+00E+0 - lim lim R 1 -dx x(x + 1) JE