 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-2/24g/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

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

 New to topics? Read the docs here!