B 1 = -1, which part of this proof is wrong?

Of course 1 isn't same as -1.
This proof must be wrong but I can't find which part of this proof is wrong.
Could you help me with this problem?
(1)$$1 = \sqrt{1}$$
(2)$$= \sqrt{(-1)(-1)}$$
(3)$$= \sqrt{(-1)} \cdot i$$
(4)$$= i \cdot i$$
$$=-1$$
 

symbolipoint

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Would you like better to start with [itex]i^2+1=0[/itex] ?
 

Samy_A

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HallsofIvy

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In the transition between the second line, [itex]= \sqrt{(-1)(-1)}[/itex], and the third line, [itex]= \sqrt{-1}\cdot i[/itex] you are assuming that [itex]\sqrt{ab}= \sqrt{a}\cdot \sqrt{b}[/itex]. That is true for real numbers but not for general complex numbers.
 
##1=\sqrt{1}##
##=\sqrt{(-1)(-1)}##
##=\sqrt{-1}\cdot\sqrt{-1}##
##=i^2##
##=-1##
 

DrClaude

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##1=\sqrt{1}##
##=\sqrt{(-1)(-1)}##
##=\sqrt{-1}\cdot\sqrt{-1}##
##=i^2##
##=-1##
You are just repeating what others have pointed out to be wrong.
 

LCKurtz

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In a thread that is 7 months old.
 

phinds

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And for an OP who has not been here since posting the question.
 

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