Let $S^1=\{z:|z|=1\}$. For each of the functions $f$ determine $M(f)=\sum\{|f(z)|:z\in S^1\}$, $m(f)=\inf\{|f(z)|:z\in S^1\}$, and the points $z_M$ and $z_m$ such that $|F(z_M)|=M(f)$ and $|f(z_m)|=m(f)$.
$$f(z)=\frac{z-b}{1-\bar bz}\;,\text{ where }|b|\ne 1$$
$$f(z)=\frac{z-b}{1-\bar bz}-a\;,\text{ where }|b|\ne 1\text{ and }a\ne 0$$
Translation of original title: Can you help me, I tried to transform to polar coordinates but I didn't understand the second exercise
Original Spanish:
Sea $S^{1}=\left\lbrace z: |z|=1\right\rbrace $.Para cada una de las funciones $f$ determine $ M(F)=sup\left\lbrace |f(z)|:z \in S^{1}\right\rbrace$,$m(f)=inf\left\lbrace|f(z)|:z \in S^{1} \right\rbrace$ y los puntos $z_{M} \ \text{y} \ z_{m} $ y tales que $|f(z_{M})|=M(f) $ y $|f(z_{m})|=m(f)$ $$f(z)=\dfrac{z-b}{1-\bar{b}z}\ \text{donde} \ |b| \ne 1$$ $$ f(z)=\dfrac{z-b}{1-\bar{b}z} -a \ \ \text{donde} \ |b| \ne 1 y a \neq 0$$