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Why is $1 i$ equal to $-i$? - Mathematics Stack Exchange While 1 i =i−1 1 i = i 1 is true (pretty much by definition), if we have a value c c such that c ∗ i = 1 c ∗ i = 1 then c =i−1 c = i 1 This is because we know that inverses in the complex numbers are unique
If $A A^{-1} = I$, does that automatically imply $A^{-1} A = I$? 1 Short Answer Yes AA -1 = A -1 A = I when the Det (A) ≠ ≠ 0 and A is a square matrix Long Answer A matrix is basically a linear transformation applied to some space For the sake of simplicity I will assume that we are in a 2D plane having 2 basis vectors i ^ and j ^ each having the magnitude of 1 with coordinates (1,0) and (0,1
What is the value of $1^i$? - Mathematics Stack Exchange There are infinitely many possible values for $1^i$, corresponding to different branches of the complex logarithm The confusing point here is that the formula $1^x = 1$ is not part of the definition of complex exponentiation, although it is an immediate consequence of the definition of natural number exponentiation
abstract algebra - Prove that 1+1=2 - Mathematics Stack Exchange Possible Duplicate: How do I convince someone that $1+1=2$ may not necessarily be true? I once read that some mathematicians provided a very length proof of $1+1=2$ Can you think of some way to
power series - How can we know the answer to 1-1+1-1+1 . . . The series does not converge, because as you observe, the partial sums $1,0,1,0,\ldots$ oscillate and do not approach a single limit There are various ways to assign values to some divergent series, such as Cesaro summation, regularization, etc See here for some information specific to this series