-1
votes
1answer
145 views

Complex has became so hard after the min\max modulus principle. Need some proofs and examples. [closed]

1) $f(z)$ being non constant and analytic in a domain $D$ if $f(z)$ continuous on $\overline{D}$ and $|f(z)|$ is constant on the boundary I need to prove that $f(z)$ must have a zero inside $D$! 2) ...
0
votes
1answer
41 views

Show that $\sqrt[k]{|z-a_1|\cdots |z-a_k|}$ has a max greater than $R$, and a min less than $R$

This is a homework problem. For $|z| \le R$ and $|a_j| < R$ for $j=1,\ldots, k$, not all zero, show that $\sqrt[k]{|z-a_1|\cdots |z-a_k|}$ has a max greater than $R$, and a min less than $R$. ...