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)