Question: Give the order of each of zeros of the given function.
$$Log(1-z), |z|<1$$
Answer:
Let $f(z)=Log(1-z), |z|<1$. Let $f(z_0)=0$. Then, we get that $z_0=0$.
Since, $f'(z) = \frac{-1}{1-z}$, we know that $f'(z_0) = -1 \neq 0$.
Therefore, the order of $z_0 = 0$ of the given function is $1$.
