Radius of Convergence of Power Series Expansion for Sine Function

Theorem
The sine function has the complex power series expansion:

which is the power series expansion of the sine function.

This is valid for all $z \in \C$.

Proof
Applying Radius of Convergence from Limit of Sequence: Complex Case, we find that:

Hence the result.

Also see

 * Power Series Expansion for Sine Function