## Modulus (Complex Number)

The modulus of a Complex Number is denoted .

 (1)

 (2)

Let and be two Complex Numbers. Then
 (3) (4)

so
 (5)

Also,
 (6) (7)

so
 (8)

and, by extension,
 (9)

The only functions satisfying identities of the form

 (10)

are , , and (Robinson 1957).

Robinson, R. M. A Curious Mathematical Identity.'' Amer. Math. Monthly 64, 83-85, 1957.