Answer
$I_1 = 8.944*e^{-0.856*j} $A
Work Step by Step
This problem is approached by using a current divider using impedance instead of regular resistance.
Calculate parallel impedance
$Z_{||} = \frac{2*(-4j)}{2-4j} \Omega$
$Z_{||} = \frac{(-4j)}{1-2j} \Omega$
Now use the current divider formula
$I_1 = 10*e^{-j*\pi /8} *\frac{Z_{||}}{Z_1}$
$I_1 = 10*e^{-j*\pi /8} *\frac{-2j}{1-2j}$
Use a calculator with complex capabilities to solve for the final current i1
$I_1 = 8.944*e^{-0.856*j} $ A
