Let the following circuit :
so we have \( I_1 + I_2 + I_3 + \frac{V_x}{0.5 \Omega} = 0 \iff \frac{V_x}{j \Omega} + \frac{V_x}{(1+j) \Omega} + \frac{V_1}{1 \Omega} + 2V_x = 0 \\\)
and we have : \( V_1 + 12(0°) + V_x = 0 \iff V_x =V_1  12(0°) \\ \)
Finally \( V_1 \approx 8.653(3.1798°) \)
so we have \( I_1 + I_2 + I_3 + \frac{V_x}{0.5 \Omega} = 0 \iff \frac{V_x}{j \Omega} + \frac{V_x}{(1+j) \Omega} + \frac{V_1}{1 \Omega} + 2V_x = 0 \\\)
and we have : \( V_1 + 12(0°) + V_x = 0 \iff V_x =V_1  12(0°) \\ \)
Finally \( V_1 \approx 8.653(3.1798°) \)
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