Complex Inverse Sine/Examples/2

Examples of Complex Inverse Sine Function

 * $\sin^{-1} \paren 2 = \dfrac {4 k + 1} 2 \pi - i \ln \paren {2 \pm \sqrt 3}$

for $k \in \Z$.

Proof
By definition of complex inverse sine:
 * $\sin^{-1} \paren 2 := \set {z \in \C: \sin z = 2}$

Thus: