Question with solving for complex power, S, for each component
To get complex power, you first need to get voltage on the three components after R1. You can calculate it like a voltage divider, when you first combine impedances of R2,C1,L1. \$Z_{L_1}=j\omega L_1=10j\Omega\$, \$Z_{C_1}=\frac{1}{j\omega C_1}=-0.1j\Omega\$, \$Z_{R_2}=1\Omega\$. Make inverse terms to get admittance, add them and invert again. \$Z_{R_2,C_1,L_1}=\frac{10j}{10j-99}\Omega\$. RMS voltage of source is \$\frac{2}{\sqrt{2}}\mathrm{V}\$, scaled by \$\dfrac{\frac{10j}{10j-99}}{\frac{10j}{10j-99}+1}\$ it is \$\frac{200\sqrt{2}}{10201}-\frac{990\sqrt{2}}{10201}i\, \mathrm{V}\$.

Now you can start with power calculation. \$S=V\cdot I^*=\frac{V\cdot V^*}{Z^*}\$, \$S_{L_1}=\frac{20}{10201}i\, \mathrm{VA}\$, \$S_{C_1}=-\frac{2000}{10201}i\, \mathrm{VA}\$, \$S_{R2}=\frac{200}{10201}\, \mathrm{VA}\$

Last thing is the power at R1. Voltage at it is \$\frac{2}{\sqrt{2}} \cdot \dfrac{1}{\frac{10j}{10j-99}+1}=\frac{10001\sqrt{2}}{10201}+\frac{990\sqrt{2}}{10201}i\, \mathrm{V}\$, and \$S_{R_1}=\frac{19802}{10201}\, \mathrm{VA}\$.