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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
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
factorial - Why does 0! = 1? - Mathematics Stack Exchange Intending on marking as accepted, because I'm no mathematician and this response makes sense to a commoner However, I'm still curious why there is 1 way to permute 0 things, instead of 0 ways
Arithmetic pattern $1 + 2 = 3$, $4 + 5 + 6 = 7 + 8$, and so on The other interesting thing here is that 1,2,3, etc appear in order in the list And you have 2,3,4, etc terms on the left, 1,2,3, etc terms on the right This should let you determine a formula like the one you want Then prove it by induction
If $A A^{-1} = I$, does that automatically imply $A^{-1} A = I$? This is same as AA -1 It means that we first apply the A -1 transformation which will take as to some plane having different basis vectors If we think what is the inverse of A -1 ? We are basically asking that what transformation is required to get back to the Identity transformation whose basis vectors are i ^ (1,0) and j ^ (0,1)