Sine Function is Absolutely Convergent/Complex Case/Proof 2

Theorem
Let $z \in \C$ be a complex number.

Let $\sin z$ be the sine of $z$.

Then:


 * $\sin z$ is absolutely convergent for all $z \in \C$.

Proof
Radius of Convergence of Power Series Expansion for Sine Function shows that the radius of convergence of the complex sine function is infinite.

Then Existence of Radius of Convergence of Complex Power Series shows that the complex sine function is absolutely convergent.