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bergausstein
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is this a difference of two squares?
$\displaystyle x^{\frac{1}{4}}-y^{\frac{1}{4}}$
$\displaystyle x^{\frac{1}{4}}-y^{\frac{1}{4}}$
MHB What is the Difference of Two Squares in this Expression?
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The expression x^(1/4) - y^(1/4) can be recognized as a difference of two squares. It can be rewritten as (x^(1/8))^2 - (y^(1/8))^2. This transformation allows for the application of the difference of squares formula. The discussion confirms that this expression fits the criteria for the difference of two squares. Understanding this concept is essential for simplifying and factoring similar expressions.
Obviously, there is something elementary I am missing here.
To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix
in the real plane; taking the transpose we get
which then corresponds to a-bi...