The currents in a \(\Delta\) load are \(I_{a b}=10 \angle 0^{\circ}, I_{b c}=12 \angle-90^{\circ}\), and \(I_{c a}=15 \angle 90^{\circ} \mathrm{A}\). Calculate

(a) the sequence components of the \(\Delta\)-load currents, denoted \(I_{\Delta 0}, I_{\Delta 1}\), and \(I_{\Delta 2}\);

(b) the line currents \(I_{a}, I_{b}\), and \(I_{c}\), which feed the \(\Delta\) load; and

(c) sequence components of the line currents \(I_{\mathrm{L} 0}, I_{\mathrm{L} 1}\), and \(I_{\mathrm{L} 2}\). Also, verify the following general relation: \(I_{\mathrm{L} 0}=0, I_{\mathrm{L} 1}=\sqrt{3} I_{\Delta 1} /-30^{\circ}\), and \(I_{\mathrm{L} 2}=\sqrt{3} I_{\Delta 2} \angle+30^{\circ}\).