Complex Analysis: Theory and Applications · Problem 5.5.1

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · inverse-trig-hyperbolic

Problem

Find all values of the following. (a) arcsin⁡54\arcsin \dfrac{5}{4}. (b) arccos⁡53\arccos \dfrac{5}{3}. (c) arcsin⁡3\arcsin 3. (d) arccos⁡3i\arccos 3i. (e) arctan⁡2i\arctan 2i. (f) arctan⁡i\arctan i. (g) arcsinh⁡i\operatorname{arcsinh} i. (h) arcsinh⁡34\operatorname{arcsinh} \dfrac{3}{4}. (i) arccosh⁡i\operatorname{arccosh} i. (j) arccosh⁡12\operatorname{arccosh} \dfrac{1}{2}. (k) arctanh⁡i\operatorname{arctanh} i. (l) arctanh⁡i3\operatorname{arctanh} i\sqrt{3}.

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