Use mesh analysis to find Vo in the circuit shown in the fig

Use mesh analysis to find Vo in the circuit shown in the figure below.

Use mesh analysis to find V_0 in the circuit shown in the figure below. Enter the amplitude and the phase angle. The phase angle must be in the interval (-180 degree, 180 degree].

Solution

from the circuit i2=-4<90 amps

apply kvl to loop current i1

-12<0+8i1+(-j8)(i1+4<90)+4(i1+4<90)=0

i1[8+4-j8]=12<0+j8*4<90-16<90

i1=1.775<-107.65 amps

vo=4(i1-i2)=4(1.775<-107.65+4<90)

vo=9.4818<103.122 volts

magnitude=9.4818

phase angle=103.122 degrees.