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

Byeonggon Lee

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

Homework Helper
Gold Member
Would you like better to start with $i^2+1=0$ ?

Samy_A

Homework Helper
• Demystifier

HallsofIvy

Homework Helper
In the transition between the second line, $= \sqrt{(-1)(-1)}$, and the third line, $= \sqrt{-1}\cdot i$ you are assuming that $\sqrt{ab}= \sqrt{a}\cdot \sqrt{b}$. That is true for real numbers but not for general complex numbers.

Deepak suwalka

$1=\sqrt{1}$
$=\sqrt{(-1)(-1)}$
$=\sqrt{-1}\cdot\sqrt{-1}$
$=i^2$
$=-1$

DrClaude

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

LCKurtz

Homework Helper
Gold Member
In a thread that is 7 months old.

phinds

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

dkotschessaa

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

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