Answer
$I_3 = 20cos(377t - 0.192)$ A
Work Step by Step
This problem looks complex at first complex, but it is easy once you realize that since the components are in parallel. Component 3 has a known voltage and impedance so a current can easily be calculated with $V = I * R$ where R is our impedance
$V_{tot} = 340cos(377t) $V
$I_{3}(jw) = V_{tot} / Z_3 = \frac{340}{17e^{j*0.192}}$
$I_3 = 20cos(377t - 0.192)$ A
