@Gianluca Gorni you could simplify your version to

Sum[Inactive[Power][3, i], {i, 1, 10}]

If @RAY LAWICKI wants nice typesetting this could work:

Sum[Superscript[3, i], {i, 1, 10}]

with further evaluation triggered as

% /. Superscript -> Power

You can try this way:

Inactive[Plus] @@ 
 Table[Inactive[Power][3, 
   i], {i, {1, 2, 3, \[CenterEllipsis], i, \[CenterEllipsis], 100}}]

I think there is no built-in function for exactly the thing you need. The closest is AbsArg. You can build the exponential from there:

AbsArg[2 - 2 I] /. {r_, t_} :> r*Exp[I*t]
Abs[2 - 2 I] Exp[I*Arg[2 - 2 I]]

You can define your own function:

ConvertToExponential[z_] := Abs[z] Exp[I*Arg[z]]

thank you for your suggestion ray.

You could write

f[x_] := x^2 - x + 3;
Plot[#[[2]], {x, -6, 6}, PlotRange -> 15,    PlotStyle -> #[[1]]] 
& /@ {{Red, f[x]}, {Green, f[2 x]}, {Blue,    f[x - 2]}, {Orange, -2 f[x]}}

as well, if you prefer to use /@ instead @@@. /@ is the shortcut for Map[ ] and applies the function to each element of first level in the list. Here each of these elements will be a list again such as{Red, f[x]}.

By the way: Simply writing #1 and #2 won't be succesfull. You need the subscription given by the brackets [[ ]].

thanks it does work but I do not understand the following bits of the code #2 what does this do and &@@@ what does this mean and why do we have #1 in plotstyle? being only a beginner I some times do not understand the effect of the above. ray.

This seem to work

f[x_]:=x^2-x+3;
Plot[#2,{x,-6,6},PlotRange->10,PlotStyle->#1]&@@@{{Red,f[x]},{Green,f[2 x]},{Blue,f[x-2]},{Orange,-2f[x]}}

MY MATHEMATICA IS VERSION 10.0 AND IT DOES WORK FINE BECAUSE I JUST REALISED THAT I WAS USING && RATHER THAN @@ SO THANKS AGAIN. Can you explain how that code works as I don't understand the use of @@ in the line and why I cannot use I! rather the the word factorial. Also I am trying to plot a series of separate graphs in different colour but my code is not working correctly eg I define f(x)=x^2-x+3 (say) ,then Table[Plot[f,{x,-6,6},PlotRange->10],{f,[f(x],f[2x],f[x-2],-2f{x]}}] which produces a table of the graphs but if I now include PlotStyle->{Red,Green,Blue,Orange} I get no graphs.
ray.

thanks for the hint however it does not produce + signs between the elements ,what I wanted was an output as ( 1!)^1+(2!)^2+(3!)^3+(4!)^4..... help ray