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Replies: 9   Last Post: Oct 17, 2013 12:03 PM

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 Nasser Abbasi Posts: 6,677 Registered: 2/7/05
Posted: Oct 14, 2013 7:37 PM

On 10/14/2013 1:30 PM, clicliclic@freenet.de wrote:
>
> Over which extended region of complex numbers a and b does the relation
>
> ABS(a^2*ABS(b - a)^2 + ABS(a)^2*(b^2 - a^2))
> = ABS(a)*ABS(b - a)*(ABS(a)^2 + ABS(b)^2 - ABS(b - a)^2)
>
> hold?
>
> Martin.
>

Mathematica V 9.01, says

-----------------
eq = Abs[a^2*Abs[b - a]^2 + Abs[a]^2*(b^2 - a^2)] ==
Abs[a]*Abs[b - a]*(Abs[a]^2 + Abs[b]^2 - Abs[b - a]^2)

Reduce[eq, {a, b}]
----------------------

(

Re[a] < 0 && ((Im[a] < 0 && Im[b] <= -((Re[a] Re[b])/Im[a]))

|| (Im[a] == 0 && Re[b] <= 0)

|| (Im[a] > 0 && Im[b] >= -((Re[a] Re[b])/Im[a]))))

|| (Re[a] == 0 && ((Im[a] < 0 && Im[b] <= 0)

|| Im[a] == 0

|| (Im[a] > 0 && Im[b] >= 0)))

|| (Re[a] > 0 && ((Im[a] < 0 && Im[b] <= -((Re[a] Re[b])/Im[a]))

|| (Im[a] == 0 && Re[b] >= 0)

|| (Im[a] > 0 && Im[b] >= -((Re[a] Re[b])/Im[a])))

)

---------------------------------------

I am not good in Maple, so there might be better
command to handle this in than solve, but this is what solve
gives in Maple 17:

------------------------------------
eq:=Abs(a^2*Abs(b - a)^2 + Abs(a)^2*(b^2 - a^2))=
Abs(a)*Abs(b - a)*(Abs(a)^2 + Abs(b)^2 - Abs(b - a)^2);

solve(eq,{a,b});

{
a = a,

b = RootOf(Abs(a)^3*Abs(_Z-a)-Abs(a)*Abs(_Z-a)^3
+Abs(a)*Abs(_Z-a)*Abs(_Z)^2-Abs(Abs(a)^2*_Z^2
-Abs(a)^2*a^2+a^2*Abs(_Z-a)^2))
}

-------------------------

--Nasser

Date Subject Author
10/14/13 clicliclic@freenet.de
10/14/13 Nasser Abbasi
10/15/13 clicliclic@freenet.de
10/16/13 A N Niel
10/16/13 Nasser Abbasi
10/17/13 A N Niel
10/15/13 Axel Vogt
10/15/13 clicliclic@freenet.de
10/16/13 A N Niel
10/17/13 clicliclic@freenet.de