\begin{aligned} &I_{1}=\frac{V_{A}-V_{B}}{Z_{L}}\\ &I_{2}=\frac{V_{A}}{R_{2}+Z_{C}}\\ &I_{4}=\frac{V_{B}}{R_{4}}\\ &\begin{array}{ll} I-I_{1}-I_{2}=0 & I-\frac{V_{A}-V_{B}}{Z_{L}}-\frac{V_{A}}{R_{2}+Z_{C}}=0 \\ I_{1}-I_{3}-I_{4}=0 & \frac{V_{A}-V_{B}}{Z_{L}}-\frac{V_{B}+U_{S}}{R_{3}}-\frac{V_{B}}{R_{4}}=0 \end{array}\\ &V_{A} \cdot\left(\frac{1}{Z_{C}+R_{2}}+\frac{1}{Z_{L}}\right)+V_{B} \cdot\left(-\frac{1}{Z_{L}}\right)=I\\ &V_{B} \cdot\left(\frac{1}{R_{3}}+\frac{1}{Z_{L}}+\frac{1}{R_{4}}\right)+V_{A} \cdot\left(-\frac{1}{Z_{L}}\right)=\frac{-U_{s}}{R_{3}}\\ &\left[\begin{array}{cc} \frac{1}{Z_{C}+R_{2}}+\frac{1}{Z_{L}} & -\frac{1}{Z_{L}} \\ -\frac{1}{Z_{L}} & \frac{1}{R_{3}}+\frac{1}{Z_{L}}+\frac{1}{R_{4}} \end{array}\right] \cdot\left[\begin{array}{c} V_{A} \\ V_{B} \end{array}\right]=\left[\begin{array}{c} I \\ -U_{s} \\ R_{3} \end{array}\right]\\ &\left[\begin{array}{cc} \frac{1}{Z_{C}+R_{2}}+\frac{1}{Z_{L}} & -\frac{1}{Z_{L}} \\ -\frac{1}{Z_{L}} & \frac{1}{R_{3}}+\frac{1}{Z_{L}}+\frac{1}{R_{4}} \end{array}\right] \cdot\left[\begin{array}{c} V_{A} \\ V_{B} \end{array}\right]=\left[\begin{array}{c} I \\ \frac{-a \cdot U_{L}}{R_{3}} \end{array}\right]=\left[\begin{array}{c} I \\ \frac{-a \cdot\left(V_{A}-V_{B}\right)}{R_{3}} \end{array}\right]\\ &I_{1}=\frac{V_{A}-V_{B}}{Z_{L}} \quad U_{L}=I_{1} \cdot Z_{L}=V_{A}-V_{B} \end{aligned} \begin{aligned} &\left[\begin{array}{cc} \frac{1}{Z_{C}+R_{2}}+\frac{1}{Z_{L}} & -\frac{1}{Z_{L}} \\ -\frac{1}{Z_{L}}+\frac{a}{R_{3}} & \frac{1}{R_{3}}+\frac{1}{Z_{L}}+\frac{1}{R_{4}}-\frac{a}{R_{3}} \end{array}\right] \cdot\left[\begin{array}{l} V_{A} \\ V_{B} \end{array}\right]=\left[\begin{array}{l} I \\ 0 \end{array}\right]\\ &\omega=1\\ &I=5 \cdot e^{1 j \cdot 30 d e g}=4.33+2.5 \mathrm{i}\\ &U_{s}=a \cdot U_{L}\\ &Z_{L}:=1 \mathrm{j} \cdot \omega \cdot L=8 \mathrm{i} \quad Z_{C}:=-1 \mathrm{j} \cdot \frac{1}{\omega \cdot C}=-5 \mathrm{i}\\ &\left[\begin{array}{c} V_{A} \\ V_{B} \end{array}\right]:=\left[\begin{array}{cc} \frac{1}{Z_{C}+R_{2}}+\frac{1}{Z_{L}} & -\frac{1}{Z_{L}} \\ -\frac{1}{Z_{L}}+\frac{a}{R_{3}} & \frac{1}{R_{3}}+\frac{1}{Z_{L}}+\frac{1}{R_{4}}-\frac{a}{R_{3}} \end{array}\right]^{-1} \cdot\left[\begin{array}{l} I \\ 0 \end{array}\right]=\left[\begin{array}{c} 32.771+21.671 \mathrm{i} \\ 3.886-8.535 \mathrm{i} \end{array}\right]\\ &I_{1}=\frac{V_{A}-V_{B}}{Z_{L}}=3.776-3.611 \mathrm{i}\\ &I_{2}=\frac{V_{A}}{R_{2}+Z_{C}}=0.554+6.111 \mathrm{i}\\ &I_{3}=\frac{V_{B}+a \cdot U_{L}}{R_{3}}=1.833+0.657 \mathrm{i}\\ &I_{4}=\frac{V_{B}}{R_{4}}=1.943-4.267 \mathrm{i} \end{aligned} \begin{aligned} &U_{S}:=a \cdot U_{L}=14.443+15.103 \mathrm{i} \\ &I-\frac{V_{A}-V_{B}}{Z_{L}}-\frac{V_{A}}{R_{2}+Z_{C}}=0 \\ &\frac{V_{A}-V_{B}}{Z_{L}}-\frac{V_{B}+U_{S}}{R_{3}}-\frac{V_{B}}{R_{4}}=0 \\ &I_{2} \cdot R_{2}+I_{2} \cdot Z_{C}-I_{1} \cdot Z_{L}+a \cdot I_{1} \cdot Z_{L}-I_{3} \cdot R_{3}=0 \end{aligned}