Mathematics · Complex Analysis
Let Ω be a non-empty open connected subset of ℂ and f: Ω → ℂ be a non-constant function. Let the functions f2: Ω → ℂ and f3: Ω → ℂ be defined by f2(z) = (f(z))2 and f3(z) = (f(z))3 for z ∈ Ω. Consider the following two statements: S1: If f is continuous in Ω and f2 is analytic in Ω, then f is analytic in Ω. S2: If f2 and f3 are analytic in Ω, then f is analytic in Ω. Which one of the following is correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Neither S1 nor S2 is TRUE
- 2Both S1 and S2 are TRUE✓
- 3S2 is TRUE and S1 is FALSE
- 4S1 is TRUE and S2 is FALSE
Correct answer
Both S1 and S2 are TRUE
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