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

  1. Mar 31, 2016 #1
    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)$$= i \cdot i$$
  2. jcsd
  3. Mar 31, 2016 #2


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    Would you like better to start with [itex]i^2+1=0[/itex] ?
  4. Mar 31, 2016 #3


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    Read this insight article by @micromass : https://www.physicsforums.com/insights/things-can-go-wrong-complex-numbers/
  5. Mar 31, 2016 #4


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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.
  6. Nov 25, 2016 #5
  7. Nov 25, 2016 #6


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    You are just repeating what others have pointed out to be wrong.
  8. Nov 25, 2016 #7


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    In a thread that is 7 months old.
  9. Nov 25, 2016 #8


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    And for an OP who has not been here since posting the question.
  10. Nov 25, 2016 #9
  11. Dec 13, 2016 #10
    It's ok.
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