Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 2 / 24G / i

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- Solution i

Solution

No. For example, let

f (z) = max (1 - ∣ z ∣, 0), g (z) = max (1 - ∣ z - 3∣, 0) .

Both functions are continuous and nonzero, but their supports lie in disjoint closed unit discs. Hence

f (z) g (z) = 0

for every

z \in C

.

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