Adding phasers in a parallel circuit problem
I think the question was to find the currents using rectangular calculation only and then to verify using the polar form (phasors). You need to do the calculations using rectangular coordinates and polar separately.

There are a few mistakes in the calculations shown in your post.


The impedance offered by a capacitor with reactance \$X_C\$ is \$-jX_C\$. So the impedance offered by branch1 is 6-3j.
\$A_1\angle\theta_1 + A_2 \angle \theta_2 \ne (A_1 + A_2)\angle (\theta_1 + \theta_2)\$