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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
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
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 The formal moral of that example is that the value of 1i 1 i depends on the branch of the complex logarithm that you use to compute the power You may already know that 1 =e0+2kiπ 1 = e 0 + 2 k i π for every integer k k, so there are many possible choices for log(1) log (1)
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
False Proof of 1=-1 - Mathematics Stack Exchange 1 Indeed what you are proving is that in the complex numbers you don't have (in general) $$\sqrt {xy}=\sqrt {x}\sqrt {y}$$ Because you find a counterexample
What does $QAQ^{-1}$ actually mean? - Mathematics Stack Exchange I'm self-learning Linear Algebra and have been trying to take a geometric approach to understand what matrices mean visually I've noticed this matrix product pop up repeatedly and can't seem to de