Polar form

Polar form

For any complex number z, with absolute value ${\displaystyle r=|z|}$ and argument ⁠${\displaystyle \varphi =\operatorname {arg} z}$⁠, the equation $${\displaystyle z=r(\cos \varphi +i\sin \varphi )}$$ holds. This identity is referred to as the polar form of z. It is sometimes written as ⁠${\displaystyle z=r\operatorname {\mathrm {cis} } \varphi }$⁠ or ⁠${\displaystyle z=r\exp \varphi i}$⁠. In electronics, one represents a phasor with amplitude r and phase φ in angle notation:$${\displaystyle z=r\angle \varphi .}$$