Attached is the schematic.

\(Z_C = -j2000 \\
Z_L = j1000\)
--------------------------------
\(56.56 = (1500 + j1000)i_1 - j1000i_2 \\
0 = -j1000i_1 + (1000 - j1000)i_2\)
--------------------------------
\(1000\angle90^{\circ}i_1 = 1414.21\angle-45^{\circ}i_2 \\
1_1 = 1.41421\angle-135^{\circ}i_2\)
--------------------------------
\(56.56 = 1802.78\angle33.69^{\circ}(1.41421\angle-135^{\circ})i_2 - j1000i_2 \\
= 2549.51\angle-101.31^{\circ}i_2 - j1000i_2 \\
= (-500 - j2500)i_2 - j1000i_2 \\
= (-500 - j3500)i_2 \\
= 3535.53\angle261.87^{\circ}i_2 \\
i_2 = 0.01600\angle98.1301^{\circ} = -0.0022624 + j0.01357\)
--------------------------------
\(i_1 = 1.41421\angle-135^{\circ}(0.01600\angle98.1301^{\circ}) \\
= 0.022624\angle-36.8699^{\circ} = 0.018099 - j0.01357\)
--------------------------------
\(I_s = i_1 = 0.022624\angle-36.8699^{\circ} \\
I_C = i_2 = 0.01600\angle98.1301^{\circ} \\
I_L = i_1 - i_2 = 0.018099 - j0.01357 + 0.0022624 - j0.015837 \\
= 0.0203614 - j0.029407 \\
= 0.03577\angle55.301^{\circ}\)
--------------------------------

\(I_C\) is the only one that is correct. The other two are out of phase by \(180^\circ\). However, their magnitudes are correct.

 

11-12th line down you have

56.56 = (3535.53 @ 261.87°) i2

hence

i2= 0.016 @ 98.13°

why not .....

i2 = 0.016 @ -261.87°

 

No problem - your values are OK for i2 since +98.13° is the same as -261.87°.

I think the problem occurs when you convert the polar form of i2 to rectangular form.

I have ....

i2 = .016 @ angle(98.13°) = -.00226 +j 0.01584

whereas you have ....

i2 = -.00226 +j 0.01357