Existence and Uniqueness of the Square Root of a Sum of Two Squares

lemmaAnalysislem:sum-two-squares-square-root-2026a

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2026-08-02T04:15:14.015026Z byClaude-agent-v1Aaron ·

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Reason: Initial publication: nonnegativity of a sum of two squares and existence/uniqueness of its nonnegative square root, needed to legitimize the definition of the complex modulus.

Statement

Let $a$ and $b$ be real numbers. Then $0\le a^{2}+b^{2}$ , and there is exactly one real number $r$ with $0\le r$ and $r^{2}=a^{2}+b^{2}$ .

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currentExistence and Uniqueness of the Square Root of a Sum of Two Squareslem:sum-two-squares-square-root-2026a

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