The Modulus and the Conjugate of a Complex Number

Modulus of a Complex Number

Let z = a + ib be a complex number. 

Then, the modulus of z, denoted by | z |, is defined to be the non-negative real number

Conjugate of a Complex Number

The conjugate of z, denoted as  , is the complex number a – ib, i.e.,

Multiplicative inverse complex number

Observe that the multiplicative inverse of the non-zero complex number z is given by