Re: complex equation
- To: mathgroup at smc.vnet.net
- Subject: [mg118467] Re: complex equation
- From: DC <b.gatessucks at gmail.com>
- Date: Fri, 29 Apr 2011 07:30:44 -0400 (EDT)
- Reply-to: comp.soft-sys.math.mathematica at googlegroups.com
If you're after complex solutions you might first expand your lhs with
ComplexExpand[Sqrt[1 - (x + I y)^2], TargetFunctions -> {Re, Im}]
and then try
FindRoot[{(4 x^2 y^2 + (1 - x^2 + y^2)^2)^(1/4)
Cos[1/2 ArcTan[1 - x^2 + y^2, -2 x y]] ==
2, (4 x^2 y^2 + (1 - x^2 + y^2)^2)^(1/4)
Sin[1/2 ArcTan[1 - x^2 + y^2, -2 x y]] == 0}, {{x,0}, {y, Sqrt[
3]}}]
Also, notice that :
Reduce[Sqrt[1 - (x + I y)^2] == 2, {x, y}] gives
y == -Sqrt[3] + I x || y == Sqrt[3] + I x
while
Reduce[Sqrt[1 - (x + I y)^2] == -2, {x, y}] gives
False
-Francesco