Algebraic Function/Examples/Square Root

Examples of Algebraic Functions

Let $f: \C \to \C$ be the complex function:

$\forall z \in \C: \map f z = z^{1/2}$

Then $f$ is an algebraic function.

Proof

We have that $w = z^{1/2}$ is a solution to the polynomial equation:

$w^2 - z = 0$

The result follows.

$\blacksquare$

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: The Elementary Functions: $10$