Re: complex equation
- To: mathgroup at smc.vnet.net
- Subject: [mg118447] Re: complex equation
- From: Gary Wardall <gwardall at gmail.com>
- Date: Thu, 28 Apr 2011 06:36:32 -0400 (EDT)
- References: <ip8o5p$pfi$1@smc.vnet.net>
On Apr 27, 4:38 am, Antonio Mezzacapo <ant.mezzac... at gmail.com> wrote:
> Hi everyone,
> I have a question. Do you know why Mathematica finds solution to this equation
> Solve[Sqrt[1 - z^2] = 2, z]
> {{z -> -I Sqrt[3]}, {z -> I Sqrt[3]}}
> while if I change sign of the right part it doesn't find solution anymore?
> Solve[Sqrt[1 - z^2] = -2, z]
> {}
>
> Is this related to the phase specification for complex numbers?
>
> Thank you
> Antonio Mezzacapo
Antonio,
Sqrt[1 - z^2] = -2
has no solutions, real or complex. That is the solution set is empty.
Mathematica is correct when it yields {}.
Note:
Sqrt[1 - z^2] = -2
(Sqrt[1 - z^2] )^2 = (-2)^2
1 - z^2 = 4
- z^2 = 3
z^2 =- 3
z = -i Sqrt[3] or z= i Sqrt[3]
Checking/Proving:
Sqrt[1 - (-i Sqrt[3])^2] = -2
2 = -2 NO!
Sqrt[1 - (i Sqrt[3])^2] == -2
2 = -2 NO!
Gary Wardall