Reconsider Problem 8.8 and choosing \(V_{b c}\) as the reference, show that

\[
V_{b c, 0}=0 ; \quad V_{b c, 1}=-j \sqrt{3} V_{a, 1} ; \quad V_{b c, 2}=j \sqrt{3} V_{a, 2}
\]

Problem 8.8

Let an unbalanced, three-phase, Y-connected load (with phase impedances of \(Z_{a}, Z_{b}\), and \(Z_{c}\) ) be connected to a balanced three-phase supply, resulting in phase voltages of \(V_{a}, V_{b}\), and \(V_{c}\) across the corresponding phase impedances.

Choosing \(V_{a b}\) as the reference, show that

\[
V_{a b, 0}=0 ; \quad V_{a b, 1}=\sqrt{3} V_{a, 1} e^{j 30^{\circ}} ; \quad V_{a b, 2}=\sqrt{3} V_{a, 2} e^{-j 30^{\circ}}
\]