Real and imaginary parts of $\sin z$ and $\cos z$ and their unboundedness

1. Express sin z in the form \(u + i v\) . Do the same for cos z.

2. Show that there exists a sequence \(z _ { n }\) such that sin \(z _ { n } \to \infty\) . Do the same for cos z.

(This shows that unlike their real counter parts, sin z and cos z are unbounded.)