Is statement is entire or not entire?

Question

Is the following statement is correct or incorrect ?

let $f\colon\mathbb{C} \longrightarrow \mathbb{C}$ be a function

my try : this statement is true because here partial derivative exist and its satisfied the cauchy riemann equation...so it will be analytics that mean it will be entire.

Is my answer is correct or incorrect ,,pliz verified and tell me the solution i would be more thankful...

Answer 1

No, it is not true. Take, for instance, $f(z)=\operatorname{Re}(z)$. So, $f_1(x,y)=x$ and $f_2(x,y)=0$. The function $f$ is not differentiable.