Let $f: \R \to \R$ be a real function.
Let $\map f x = y$.
Then $x$ is referred to as an independent variable.
Let $f: \C \to \C$ be a complex function.
Let $\map f z = w$.
Then $z$ is referred to as an independent variable (of $f$).
Also known as
An independent variable can also be referred to as an argument.
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 $x$.