U=220 volts=220@0° volts

Xc=40 Ohm
Zc=j40 Ohm=40@90° Ohm

Ic=U/Zc=220/(j40)=(220@0°)/(40@90°)=5.5@-90° A

 

Hello,

If you'd like to work this out with complex numbers, you can find the inductance with;
L=XL/(2*pi*f)

and the capacitor value with:
C=1/(2*pi*f*XC)

The impedances are then:
ZC=1/(j*w*C)

and
ZL=j*w*L

You can then put the inductor in series with the resistor:
Z1=j*w*L+R

and then put that in parallel with the capacitor to get the total impedance:
Z=Z1||ZC=(j*w*L+R)*(1/(j*w*C))/(j*w*L+R+1/(j*w*C))

You can then calculate the total current and other quantities.

 

is this right?

What is α (alpha) supposed to be?

How are you evaluating cos(-8.08) in your next to last line? As near as I can tell you didn't know how to deal with it so you simply ignored it all together? Does that sound like a reasonable way to go about things?