Norton  Thévenin equivalents with complex impedances
If you imagine a load attached to the circuit, to get the equivalent the current and voltage sourced to the load needs to be the same if you change the circuit.

If we go from the Thevenin to the Norton equivalent we get this current at the load:

\$ V_t = Z_t*I_n \$ 

and equivalently to go back

\$ \frac{V_t}{Z_t} = I_n \$

The transform for the impedance is:

\$ Z_t= \frac{1}{Y_n} \$

These still work for phasors because complex operations are equivalent and because Ohms law and Kirchoffs laws can be extended to phasors/complex operations.







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