To convert a number from complex form to polar form you have simply to apply the definitions of sin and cos.
First of all we use the real part of the number (3sqrt(3)) as the x coordinates and the imaginary part (without the i, so only 3) as the y and we put this on two axis as in the figure.
The polar form is nothing but r and theta.
r can be obtained easily applying the Pitagora's theorem:
r=sqrt((3sqrt(3))^2+3^2)=sqrt(27+9)=sqrt(36)=6.
theta can be calculated using the definition of cosine or sine.
We know that x=rcos(theta) and y=rsin(theta). We could then say, for example, that sin(theta)=y/r and then theta=arcsin(y/r).
In the same way we can say theta=arccos(x/r). But my favorite consists in dividing the two coordinates having
y/x=sin(theta)/cos(theta) and because sin(theta)/cos(theta)=tan(theta) we have y/x=tan(theta) and finally
theta=arctan(y/x). In our case theta=arctan(3/{3sqrt(3)})=arctan(1/sqrt(3))\approx0.52.
Then your polar coordinates are (6, 0.52).
To see if the result is correct, you can transform back your number as:
rcos(theta)+irsin(theta) = 6cos(0.52)+i*6sin(0.52)=5.19+3i and 5.19 is the approximation of 3sqrt(3).