Hi Alessandro,

you could use Graphics to visualise your complex vector. In the following I refer to this picture:

1. x = r*Cos[\[Theta]],
2. y = r*Sin[\[Theta]].
3. P=x+I*y, where I represents the imaginary unit

First we define a function which gives us a an arrow from the origin to the Point P:

ComplexVector[r_, \[Theta]_] := 
 Arrow[{{0, 0}, {r*Cos[\[Theta]], r*Sin[\[Theta]]}}]

If you would like to plot a straight line instead of an arrow, just exchange Arrow by Line!

Visualisation:

Graphics[{Blue, ComplexVector[1, Pi/4]}, Axes -> True, 
 AxesLabel -> {"real axis", "imaginary axis"}]

Where I choose the absolute value of our complex vector to be 1 and the angle to be 45º.

The code above is for for the use in Mathematica. If you use the Wolfram Alpha app or the Wolfram Alpha website you just can type in (for example):

1+I*2

where x=1, y=2. Beside other information a plot is provided.

You can use the relations for x and y to convert between cartesian and polar coordinates.This link will open an example, done with the Wolfram Alpha website.

Cheers,

Philipp