Definition:Independent Variable/Complex Function

Definition

Let $f: \C \to \C$ be a complex function.

Let $\map f z = w$.

Then $z$ is referred to as an independent variable (of $f$).

Linguistic Note

The terms independent variable and dependent variable arise from the idea that it is usual to consider that $x$ can be chosen independently of $y$, but having chosen $x$, the value of $y$ then depends on the value of $x$.

Sources

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