Simple way to plot a complex valued function of one real variable

How can I plot a complex valued function of one real variable, $f(t)$, as

$$x=-\Re f(t),\ z=\Im\ f(t),\ y=t \space?$$

My aim is a 3-dimensional path, treating the complex valued function as if it was a two real components vector valued function.

For example $e^{it}$ can be visualized as a helix in $\mathbb R^3$, in which, for example, the "east-west" axis ($y$) represents the single real variable: $t$, the "north-south" axis ($x$) represents $-\Re f(t)$, and the "top-down" axis ($z$) represents $\Im\ f(t)$.

• how to draw a plot of function like, f(t,y)= yExp(it) – user48251 Apr 19 '17 at 18:33

Plotting the real vs imaginary parts of $e^{ix}$ should be a circle, not a helix. Using ParametricPlot:
f[x_] := Exp[I x];

f[x_] := Exp[I x];