1=1
1=sqrt[1]
1=sqrt[(-1)*(-1)]
1=sqrt[-1]*sqrt[-1]
1=iota*iota
1=iota^2
and iota raise to the power 2 is -1
therefore
1= -1
where i made a mistake?????
help me out
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1=1
1=sqrt[1]
1=sqrt[(-1)*(-1)]
1=sqrt[-1]*sqrt[-1]
1=iota*iota
1=iota^2
and iota raise to the power 2 is -1
therefore
1= -1
where i made a mistake?????
help me out
the square root of -1 is not just iota, just as the square root of 4 is not just 2 - it is +/-2, since (-2)2 = 4 as well.Quote:
Originally Posted by monu2010
Similarly, (-iota)2 = -1, so you cannot say that sqrt[-1] = iota, you have to say that sqrt[-1] = +/-iota ("plus or minus" iota).
my dear friend u just said thatQuote:
Originally Posted by Dross
sqrt[anything]=+/-(some value)
but this time i consider only one value which is not affecting equation
u are right for this type of situation
sqrt[4]=sqrt[4]
-/+2=+/-2
then
-2=+2
then we have to cosider sign either +ve or -ve "on both the sider
my question is totally different in this case i can consider only one sign at a time.
:bigyello:
What you're doing is simply a violation of the quadratic equation. As previously mentioned, that was an artillery shell that just went off, but that's beside the point.
As previously mentioned, sqrt(4)=+/-2, and sqrt(1)=+/-1, but just because -12=1 doesn't mean that -1=1. Comprende?
Are you saying you get to choose which of +i and -i you take? Quite simply not the case.Quote:
Originally Posted by monu2010
Or, to express timeshifter's point fully, (-x)^2 = (x)^2 for all x. This does not mean that x = -x. it just means that sqrt(x^2) = +/- x.
Second line isn't true.Quote:
Originally Posted by monu2010
1 <> sqrt[1]
+/- 1 = sqrt[1]