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Topic: The cube roots of 8
Replies: 45   Last Post: Nov 14, 1999 4:24 PM

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Quentin Grady

Posts: 291
Registered: 12/6/04
Re: The cube roots of 8
Posted: Oct 7, 1999 6:13 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply




G'day G'day Folks,

By way of appreciation to all those people who showed me ways to
find the complex roots of 8 I' d like to share this application.

One of the features of three phase electricity is that it delivers
constant total power to a load.

The three phase can be named red, yellow and blue.

Power = ((v_r)^2 + (v_y)^2 + (v_b)^2 ) /R for resistive loads.

The trick is to prove (v_r)^2 + (v_y)^2 + (v_b)^2 is a constant.

Let one of the voltages be the principle root of 8 ie 2.

Letting j = sqrt(-1)
The complex roots become -1 + j*sqrt(3) and -1 - j*sqrt(3)
And v_r)^2 + (v_y)^2 + (v_b)^2 becomes 6 which is constant.

In general v_r)^2 + (v_y)^2 + (v_b)^2 = 1.5 * (V_peak)^2

It makes a nice change from the trig method.

Thanks,


On Tue, 28 Sep 1999 07:39:37 +1200, Quentin Grady
<quentin@inhb.co.nz> wrote:

>G'day G'day Folks,
>
> I grew up happy in the knowledge that the cube root of 8 was 2.
>Life was simple then. Calculators gave 2 as the answer and it was the
>only answer I thought of looking for.
>
>Then I read a statement that astounded me,
> "Every number has n nth roots."
>
>Is there a simple proof of the statement?
>
>If for the moment we assume that the statement is true then certain
>conclusions follow in an obvious fashion. Since 8 has one real cube
>root, it must have two complex number cube roots. It is easy enough
>to prove the complex cube roots by multiplication once they are found,
>
>
>My question is,
>"How does one systematically find complex roots of positive integers?"
>
>Thanks,







Date Subject Author
9/27/99
Read The cube roots of 8
Quentin Grady
9/27/99
Read Re: The cube roots of 8
Doug Norris
9/29/99
Read Re: The cube roots of 8
Quentin Grady
9/29/99
Read Re: The cube roots of 8
Doug Norris
9/27/99
Read Re: The cube roots of 8
Dann Corbit
9/27/99
Read Re: The cube roots of 8
Paul Arendt
9/29/99
Read Re: The cube roots of 8
Quentin Grady
9/27/99
Read Re: The cube roots of 8
Lynn Killingbeck
9/27/99
Read Re: The cube roots of 8
Peter Percival
9/27/99
Read Re: The cube roots of 8
spamless@nil.nil
9/29/99
Read Re: The cube roots of 8
Quentin Grady
9/27/99
Read Re: The cube roots of 8
Jim Hollerman
9/28/99
Read Re: The cube roots of 8
Robert Armagost
9/28/99
Read Re: The cube roots of 8
Jim Hollerman
9/27/99
Read Re: The cube roots of 8
James Buddenhagen
9/29/99
Read Re: The cube roots of 8
Quentin Grady
10/1/99
Read Re: The cube roots of 8
feldmann4350@my-deja.com
9/28/99
Read Re: The cube roots of 8
William L. Bahn
9/28/99
Read Re: The cube roots of 8
oholden@my-deja.com
9/28/99
Read Re: The cube roots of 8
G. A. Edgar
9/28/99
Read Re: The cube roots of 8
John Savard
9/29/99
Read Re: The cube roots of 8
Quentin Grady
9/29/99
Read Re: The cube roots of 8
Quentin Grady
9/30/99
Read Re: The cube roots of 8
spamless@nil.nil
9/30/99
Read Re: The cube roots of 8
spamless@nil.nil
9/30/99
Read Re: The cube roots of 8
Quentin Grady
9/30/99
Read Re: The cube roots of 8
Quentin Grady
10/1/99
Read Re: The cube roots of 8
spamless@nil.nil
10/7/99
Read Re: The cube roots of 8
Quentin Grady
10/7/99
Read Re: The cube roots of 8
Earle Jones
10/8/99
Read Re: The cube roots of 8
Steve McGrew
10/8/99
Read Re: The cube roots of 8
Denis Feldmann
10/8/99
Read Re: The cube roots of 8
Steve McGrew
10/10/99
Read Re: The cube roots of 8
Denis Feldmann
10/11/99
Read Re: The cube roots of 8
Mike Mccarty Sr
10/11/99
Read Re: The cube roots of 8
Mike Mccarty Sr
10/12/99
Read Re: The cube roots of 8
Steve McGrew
10/12/99
Read Re: The cube roots of 8
Lee Rudolph
10/13/99
Read Re: The cube roots of 8
Clive Tooth
10/13/99
Read Re: The cube roots of 8
Steve McGrew
10/12/99
Read Re: The cube roots of 8
feldmann4350@my-deja.com
10/12/99
Read Re: The cube roots of 8
Mike Mccarty Sr
10/13/99
Read Re: The cube roots of 8
Robin Chapman
10/15/99
Read Re: The cube roots of 8
John R Ramsden
10/12/99
Read Re: The cube roots of 8
Gary Tupper
11/14/99
Read cube roots of 8
michael cook

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