Tagged Questions
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1answer
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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
36 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 $R$.
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