In an AC circuit, the voltage E, current I, and impedance Z are related by the

Formula E = I · Z

Find the current in a circuit with voltage 14 – 8j volts and Impedance is 2 – 3j ohms.

E = I · Z

Substitute E and Z values

14 – 8j = i · (2 – 3j)

Divide each side by (2 – 3j)

Multiply the numerator and denominator by the conjugate of the denominator

2 – 3j. Conjugate of 2 – 3j is 2 + 3j.

  (Multiply the numerator using FOIL method)  (Formula: )

Evaluate powers: .

              (Multiply: )

                     (Multiply: )

Distribute terms using distributive property: .

                     (Subtract: )

               (Substitute the imaginary unit value )

                       (Product of two same signs is positive)

Apply commutative property of addition: a + b = b + a.

                                (Add: 28 + 24 = 52 and 4 + 9 = 13)

                             (Write standard division form: )

                                       (Divide: )

The current is 4 + 2j amps.