The discussion revolves around the mathematical reasoning behind the equation \( a = -a \) in a specific scenario involving square roots and complex numbers. Participants explore the implications of manipulating square roots and the conditions under which certain mathematical properties hold.
Participants express differing views on the validity of the mathematical manipulations involving square roots. While some acknowledge the restrictions on square root properties, there is no consensus on the implications of the results derived from these manipulations.
The discussion highlights limitations regarding the assumptions made about the values of \( a \), \( b \), and \( c \), particularly in relation to the nonnegativity required for certain square root properties to hold. The implications of choosing between \( +i \) and \( -i \) in complex numbers are also noted but remain unresolved.
The step above is where the problem is. You're using the property that ##\sqrt{ab} = \sqrt{a}\sqrt{b}##noahsdev said:I've been messing around with numbers (as you do) and I'm wondering why this occurs..
lets let a = b-c.
√a
= √(b-c)
=√(-(c-b))
=i√(c-b)
noahsdev said:=i√(-(b-c))
=i2√(b-c)
=-√(b-c)
=-√a
For example if you let a = 1, b = 2, and c = 1.
That makes sense. Thanks.Mark44 said:The step above is where the problem is. You're using the property that ##\sqrt{ab} = \sqrt{a}\sqrt{b}##
There are restrictions on this and some of the other square root properties - both a and b have to be nonnegative.