Consider the function $f : \mathbb { C } \rightarrow \mathbb { C }$ defined by
$$f ( a + i b ) = e ^ { a } ( \cos b + i \sin b ) , a , b \in \mathbb { R }$$
where $i$ is a square root of $-1$. Then\\
(A) $f$ is one-to-one and onto.\\
(B) $f$ is one-to-one but not onto.\\
(C) $f$ is onto but not one-to-one.\\
(D) $f$ is neither one-to-one nor onto.