# Toronto Math Forum

## MAT334--2020S => MAT334--Tests and Quizzes => Quiz 5 => Topic started by: Ziyi Wang on March 08, 2020, 06:46:48 PM

Title: Q5: TUT 0201
Post by: Ziyi Wang on March 08, 2020, 06:46:48 PM
Question: Give the order of each of zeros of the given function.
$$Log(1-z), |z|<1$$
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 $1$.