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You have three independent equations so can solve for the three unknowns, which are Io, I1, and Vo. Enter these equations into your calculator (and recall that you might need to place them in standard form first) and solve. Since your equations will contain complex numbers, they must be entered carefully to avoid errors.Give the values for the three unknown phasors that result from solving the three equations, and include the correct units.

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Answer:

The values are:

[tex]I_{o} =0.06+j0.045A[/tex]

[tex]I_{1} =0.3+j0.225A[/tex]

[tex]V_{o} =12+j9V[/tex]

Explanation:

the attached figure shows the diagram. The equation is the following:

[tex]I_{1} -I_{o} =\frac{V_{o} }{50} \\I_{1} -I_{o} -\frac{V_{o} }{50}=0[/tex] (eq. 1)

Voltage across the 40 Ω is equal:

[tex]V_{o} =40I_{1}[/tex] (eq. 2)

Applying the Kirchhoff´s voltage law:

[tex]75=I_{o} (600+j150)+I_{1} (40-j150)[/tex] (eq. 3)

Equation 1 and 2:

[tex]I_{1} =5I_{o}[/tex] (eq. 4)

Substituting in eq. 3

[tex]75=I_{o} (600+j150)+5I_{o} (40-j150)\\75=I_{o} (800-j600)\\I_{o} =\frac{75}{800-j600} =0.06+j0.045A[/tex]

Substituting in eq. 4

[tex]I_{1} =0.3+j0.225A[/tex]

Substituting in eq. 2:

[tex]V_{o} =12+j9V[/tex]

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