How to plot a function $f:\mathbb R \to \mathbb C$.

Question

How can I plot a function in $F(\mathbb R,\mathbb C)$ i.e a function from Real line to complex plane.For example how to plot $f(x)=\sqrt{x},x\in \mathbb R$.Is there any online software for that?I think it is possible to plot and visualize such functions because dimension of real line is one and that of complex plane is three,the sum not exceeding three.So if I take values on real line and consider real and complex part of the output value,then I think we can draw it,but I cannot properly figure out how exactly it would look.Some software help or pictorial help may be useful.

Answer 1

Any software that draws lines in space (such as Mathematica or GeoGebra) will do. Just consider the line $\left(t,\operatorname{Re}\bigl(f(t)\bigr),\operatorname{Im}\bigl(f(t)\bigr)\right)$, with $t\in\mathbb R$.

If, for instance, $f(t)=(t+i)^2=t^2-1+2ti$, then, using Mathematica, you get the curve from the picture below: