Stupid math facts 2: Inverse of a complex number; Application to simple impedance calculations
Given a complex number Y=a+jb then the modulus of its inverse is simply related to the modulus itself:
(1)
Also, the inverse of its argument is:
(2)
If Y=a+jb and Z=c+jd then:
(3)
If Y is the admittance of a shunt RC component then:
(4)
Sometimes |Z| and C are available from measurements and one wants to determine R, then from (1-3) and because the |Y| can be determined more easily than |Z|:
(5)
also:
(6)