In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit.
Quantitatively, the impedance of a two-terminal circuit element is the ratio of the complex representation of the sinusoidal voltage between its terminals, to the complex representation of the current flowing through it. In general, it depends upon the frequency of the sinusoidal voltage.
Impedance extends the concept of resistance to alternating current (AC) circuits, and possesses both magnitude and phase, unlike resistance, which has only magnitude.
Impedance can be represented as a complex number, with the same units as resistance, for which the SI unit is the ohm (Ω).
Its symbol is usually Z, and it may be represented by writing its magnitude and phase in the polar form |Z|∠θ. However, Cartesian complex number representation is often more powerful for circuit analysis purposes.
The notion of impedance is useful for performing AC analysis of electrical networks, because it allows relating sinusoidal voltages and currents by a simple linear law.
In multiple port networks, the two-terminal definition of impedance is inadequate, but the complex voltages at the ports and the currents flowing through them are still linearly related by the impedance matrix.
The reciprocal of impedance is admittance, whose SI unit is the siemens, formerly called mho.
Instruments used to measure the electrical impedance are called impedance analyzers.
Finding the series for the first part of the problem was easy, but for parallel, I'm not sure how to separate the real from the imaginary in the fractions after I add them together?
So, I take: ##(1/(2+3i) + 1/(1-5i)^{-1}##, and after I combine the denominators and combine all terms, I end up...