ArcTanh[x] - I ArcCsc[y] == (-((I Sqrt[1 - x^2] Sqrt[((-I) x Sqrt[1 - 1/y^2] - 1/y)^2/(1 - x^2)])/ ((-I) x Sqrt[1 - 1/y^2] - 1/y))) ArcSin[(Sqrt[1 - 1/y^2] - (I x)/y)/Sqrt[1 - x^2]] + (I Pi Sqrt[1 - x^2] Sqrt[((-I) x Sqrt[1 - 1/y^2] - 1/y)^2/(1 - x^2)])/ (2 ((-I) x Sqrt[1 - 1/y^2] - 1/y)) + I Pi (1 + (Sqrt[1 - x^2] Sqrt[((-I) x Sqrt[1 - 1/y^2] - 1/y)^2/(1 - x^2)])/ ((-I) x Sqrt[1 - 1/y^2] - 1/y)) Floor[(Arg[(I + I x)/Sqrt[1 - x^2]] + Arg[Sqrt[1 - 1/y^2] - I/y])/ (2 Pi)] - I Pi (-1 + (Sqrt[1 - x^2] Sqrt[((-I) x Sqrt[1 - 1/y^2] - 1/y)^2/(1 - x^2)])/ ((-I) x Sqrt[1 - 1/y^2] - 1/y)) Floor[-((-Pi + Arg[(I + I x)/Sqrt[1 - x^2]] + Arg[Sqrt[1 - 1/y^2] - I/y])/ (2 Pi))]

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