Questions 4 and 5 from section 4.3 of Conway's complex analysis book I'm reading the Conway's complex analysis book and I'm trying to solve theses exercises on page 80:

4.Prove that $e^{z+a}=e^ze^a$
5.Prove that $\cos(a+b)=\cos a\cos b-\sin a\sin b$

The author asks to use the corollary 3.8 which says:

Corollary 3.8: If $f$ and $g$ are analytic on a region $G$ then $f\equiv g$ iff $\{z\in G;f(z)=g(z)\}$ has a limit point in $G$.

My only guess to solve these exercises is to find a limit point of the set $\{z\in G;f(z)=g(z)\}$, where $f$ and $g$ are the RHS and LHS of the equations, but I don't know how to find them.
Just a remark, this is not a homework, as you can see in my last questions I'm using this site to study this book by my own.

For the question about 

Prove that $e^{z+a}=e^{z}e^{a}$

you only need to define two functions, $f(z)=e^{z+a}$ and $g(z)=e^{z}e^{a}$. Both functions are entire, and from real analysis, we know that $f\equiv g$ when $z\in \Bbb{R}$. But since $\Bbb{R}$ has limit points in $\Bbb{C}$, then $f\equiv g$ for all $z\in \Bbb{C}$. The same argument works for the second part of the exercise.  
