[Tutor] Complex roots
Dick Moores
rdm at rcblue.com
Fri Dec 17 02:01:42 CET 2004
Thanks. Tim Peters helped me out with his answer of 12/9.
<http://mail.python.org/pipermail/tutor/2004-December/033967.html>
Dick Moores
Jacob S. wrote at 19:27 12/15/2004:
>Finding the all the roots of a complex number shouldn't be too difficult. I
>tend to do it on paper sometimes. Maybe I can write a script to do it for me
>instead. I stongly caution you though. The methods that I show below are
>unstable and should be verified by a math web site as it has been quite a
>few months since I last used the equations. In fact, I'll almost bet they're
>wrong. If you want me to check them, I'll gladly google for the right
>equations if you want.
>
>where i == sqrt(-1)
>
>[pseudo-code]
>p = (a+bi)**n
>n = polar(p) ## polar is a function that converts rectangular coordinates
>to polar coordinates.
>radius = n[0]
>angle = n[1]
>
>1st root radius**n cis (angle/(180*n)) ## Where cis is short for
>(cos(angle) + i*sin(angle))
>2nd root radius**n cis (angle/(360*n))
>...
>qth root radius**n cis (angle/(180*q*n))
>[/pseudo-code]
>
>So saying, I would set a for i in range loop for n times to run these root
>finders through. Note unless you call some sort of polar to rectangular
>function on the roots, they will still be in polar.
>
>HTH as always,
>Jacob Schmidt
>
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