Complex Cosine Function/Examples/4 cos z = 3+i

Example of Complex Cosine Function
Let:
 * $4 \cos z = 3 + i$

Then:
 * $z = \dfrac {\paren {8 n + 1} \pi} 4 - \dfrac {i \ln 2} 2$ for $n \in \Z$

or:
 * $z = \dfrac {\paren {8 m - 1} i \pi} 4 + \dfrac {i \ln 2} 2$ for $m \in \Z$

Proof
Thus we have:

and: