Answer
$V_{out} = 110 \angle \frac{3 \pi}{4}$ V
Work Step by Step
Approach this problem by finding equivalent series impedance, given the reactance of each component.
$Z_L = 1000j \Omega$
$Z_C = 10000j \Omega$
$Z_{series} = 11000j \Omega $
Now use ohms law, v=ir
$V_{out} = 0.01e^{j\frac{\pi}{4}} *(11000e^{j\frac{\pi}{2}}) $
$V_{out} = 110e^{j \frac{3\pi}{4}} $V
