if $1>\delta>0$ and $|z-(-i)|<\delta$, then $|z|>1-\delta$.
Drawing the graph, it is easy to see that this statement is true. I cannot, however, show this algebraically using inequalities and basic properties of complex numbers.
2026-04-16 19:17:22.1776367042
if $1>\delta>0$ and $|z-(-i)|<\delta$, then $|z|>1-\delta$.
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Hint: $|z+i| > |i| - |z|$. Can you finish it now?