2
votes
4answers
202 views

$\{z\in C:|z| = |\operatorname{re}(z)| +|\operatorname{im}(z)|\}$ open or closed [duplicate]

Possible Duplicate: Proving that a complex set in open/closed/neither and bounded/not bounded I think $\{z\in C:|z| = |\operatorname{re}(z)| +|\operatorname{im}(z)|\}$ is closed. But I have ...
-4
votes
1answer
122 views

Boundedness on strips in the complex plane for functional equations [closed]

We know that the recurrence for $b>0$ (1) $f(0)=1$ (2) $f(z+1)=b{f(z)}$ has $f(z)=b^z$ as the only entire solution that is bounded on the strip $S=\{z: 0<\Re(z)\le 1\}$. The image of $S$ ...