Electrical Impedance - Complex Impedance

Impedance is represented as a complex quantity and the term complex impedance may be used interchangeably; the polar form conveniently captures both magnitude and phase characteristics,

where the magnitude represents the ratio of the voltage difference amplitude to the current amplitude, while the argument gives the phase difference between voltage and current. is the imaginary unit, and is used instead of in this context to avoid confusion with the symbol for electric current. In Cartesian form,

where the real part of impedance is the resistance and the imaginary part is the reactance .

Where it is required to add or subtract impedances the cartesian form is more convenient, but when quantities are multiplied or divided the calculation becomes simpler if the polar form is used. A circuit calculation, such as finding the total impedance of two impedances in parallel, may require conversion between forms several times during the calculation. Conversion between the forms follows the normal conversion rules of complex numbers.