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Re: complex equation

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  Re: complex equation DC <b.gatessucks@gmail.com> - 2011-04-29 11:30 +0000

#1973 — Re: complex equation

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

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