The modulus of a Complex Number is denoted .

(1) |

(2) |

(3) | |||

(4) |

so

(5) |

(6) | |||

(7) |

so

(8) |

(9) |

The only functions satisfying identities of the form

(10) |

**References**

Abramowitz, M. and Stegun, C. A. (Eds.).
*Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.*
New York: Dover, p. 16, 1972.

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

© 1996-9

1999-05-26