Hi,
Try taking a look at it in the time domain.
First, calculate the amplitude and phase shift for both the cap and inductor branches, then apply this to the time domain equations. The phase shift for the cap is 90 and for the inductor branch close to -45 degrees. The amplitude for the cap is 1, and the amplitude for the inductor branch is about 1.410 as you noted.
So the time equation for the source current could be written as:
Is=1*sin(wt-90/180*pi)+1.41*sin(wt+45/180*pi)
When you simplify this, or even just plot it, you see a single sine wave with amplitude equal to 1 and phase shift zero degrees. The phase shift of zero degrees tells us that whatever was done to the circuit to correct the power factor must have worked correctly.