e^z-e^-z=2i的解复变函数

Question

e^z-e^-z=2i的解 复变函数

Answer 1

e^z - e^-z - 2i = 0
e^2z - 2ie^z - 1 = 0
t^2 - 2it - 1 = 0,t = e^z
(t - i)^2 = 0
t = i (重根)
e^z = i = e^(iπ/2)
z = 2kπi + iπ/2
z = (4k + 1)(iπ/2),k∈Z