Editing Electrical impedance (section)

== Complex impedance<span id="phase_topic_anchor" class="anchor"></span> ==

[[File:Complex Impedance.svg|200px|thumb|right|A graphical representation of the [[Complex plane|complex impedance plane]]]]

The impedance of a two-terminal circuit element is represented as a [[Complex number|complex]] quantity <math>Z</math>. The [[Polar coordinates|polar form]] conveniently captures both magnitude and phase characteristics as

:<math>\ Z = |Z| e^{j \arg(Z) }</math>

where the magnitude <math>|Z|</math> represents the ratio of the voltage difference amplitude to the current amplitude, while the argument <math>\arg(Z)</math> (commonly given the symbol <math>\theta </math>) gives the phase difference between voltage and current. In electrical engineering, the letter <math>i</math> is used for [[Ampere|electric current]], so the [[imaginary unit]] is instead represented by the letter <math>j</math>.<ref name=":0">{{Cite book |last=Gross |first=Charles A. |url=https://www.worldcat.org/oclc/863646311 |title=Fundamentals of electrical engineering |date=2012 |publisher=CRC Press |others=Thaddeus Adam Roppel |isbn=978-1-4398-9807-9 |location=Boca Raton, FL |oclc=863646311}}</ref>{{Rp|page=21}}

In [[Cartesian plane|Cartesian form]], impedance is defined as

:<math>\ Z = R + jX</math>

where the [[real part]] of impedance is the resistance {{mvar|R}} and the [[imaginary part]] is the [[Reactance (electronics)|reactance]] {{mvar|X}}.

Where it is needed 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 [[Polar form|conversion rules of complex numbers]].