Mathematics · Complex Analysis
Let f : ℂ → ℂ be a continuous function. Then which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If f(z0) ≠ 0, then f(z) ≠ 0 for only one point in every neighbourhood of z0.
- 2If f(z0) ≠ 0, then f(z) ≠ 0 throughout some neighbourhood of z0.✓
- 3If f(z) ≠ 0 for some z in every neighbourhood of z0, then f(z0) ≠ 0.
- 4There exists M ≥ 0 such that |f(z)| ≤ M whenever |z| ≤ 1.
Correct answer
If f(z0) ≠ 0, then f(z) ≠ 0 throughout some neighbourhood of z0.
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