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# sqrt-1

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if sqrt(2)*sqrt(8) = sqrt(2*8) why isnt sqrt(-1)*sqrt(-1)=sqrt(-1*-1)

Guest Apr 24, 2017
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#1
+89826
+1

if sqrt(2)*sqrt(8) = sqrt(2*8) why isnt sqrt(-1)*sqrt(-1)=sqrt(-1*-1)

$$if\;\; \sqrt2*\sqrt8= \sqrt{2*8}\\\text{ why isn't }\quad\\ \sqrt{-1}*\sqrt{-1}=\sqrt{-1*-1}$$

The rules for real numbers often do not extend to imaginary numbers.

This is one such case.

Alan, or someone else might be able to give a better explanation.   :/

Melody  Apr 24, 2017
#2
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sqrt((-1)*(-1)) = +/-1

Guest Apr 24, 2017
#3
+75344
+1

The rule is

√a  *  √b   =   √ [ a * b]   only if a, b  ≥  0

CPhill  Apr 24, 2017

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