My progress so far is:

i converted V(t) to: v(t) = 120cos(377t -30°) just minues 90° to make it cos

then frequency is

F = 377/ 2∏

F = 60

XL = 2.pi(60)(40mH)

XL = j15.08 or (0+j15.08)

XC = - [1/(2∏(60)(50uF))]

XC = -j53.05 or 0-j53.05

then add XL and R

XLR=20 + j15.08

so this is the part i am confused...

We need to parallel XLR and XC so the equation is this

ZT = (XLR)(XC) / (XLR + XC)

is this correct? or i need to convert it to polar form? but i get infinity at :

Φ = tan^-1 (53.05 / 0 )

How to solve this?

i can solve i(t) by the formula i(t) = V/ZT

but i can't solve ZT.