The impedance Z, in ohms, of a circuit element is defined as the ratio of the phasor voltage V, in volts, across the element to the phasor current I, in amperes, through the elements. That is, Z=V/I. If the voltage across a circuit element is 33+10i volts and the current through the element is 4-5i amperes, determin the impedance.

Solution:

The impedance = V/I = (33+10i)/(4-5i)

= (33+10i)(4+5i)/(4-5i)(4+5i)

= (82+205i)/(4^2 + 5^2)

= (82+205i)/41

= 2 + 5i

So the impedance is 2 + 5i