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From: melahi_ahmed@yahoo.fr (ahmed)
Newsgroups: comp.lang.forth
Subject: Re: Complex square root of -1 : zsqrt(-1)
Date: Fri, 6 Sep 2024 07:11:18 +0000
Organization: novaBBS
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Hi,

Here is another definition for |z|.
It is based on the formula : z = |z| * exp(i*arg(z)).
One can get: |z| = z * exp(-i*arg(z)).

Here is the code:

: zarg ( z: a+bi -- ) ( f: -- theta)
    fswap fatan2
;

: |z| ( z: a+bi -- ) ( f: -- |z|)
    zdup zarg 0e 0e -1e z* ( z: -i*arg[z])
    zexp z*  ( z: z*exp(-i*arg[z])
    fdrop    ( z: --) ( f: |z|)
;

But it is slower than the defintion using pythag( about 3-6 times
(tested gforth)).

Ahmed