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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 $\Im\ f(t)$.

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up vote 3 down vote accepted

Plotting the real vs imaginary parts of $e^{ix}$ should be a circle, not a helix. Using ParametricPlot:

f[x_] := Exp[I x];
ParametricPlot[{Re[f[x]], Im[f[x]]}, {x, 0, 2 Pi}]

enter image description here

In the comments, the OP says that what he really wants is "y should be the real parameter of f, x should be the negative real part, and z should be the imaginary part." One interpretation of this is:

f[x_] := Exp[I x];
ParametricPlot3D[{-Re[f[x]], Im[f[x]], x}, {x, 0, 5 Pi}]

enter image description here

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