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- Why is $1 i$ equal to $-i$? - Mathematics Stack Exchange
11 There are multiple ways of writing out a given complex number, or a number in general Usually we reduce things to the "simplest" terms for display -- saying $0$ is a lot cleaner than saying $1-1$ for example The complex numbers are a field This means that every non-$0$ element has a multiplicative inverse, and that inverse is unique
- Formal proof for $ (-1) \times (-1) = 1$ - Mathematics Stack Exchange
Is there a formal proof for $(-1) \\times (-1) = 1$? It's a fundamental formula not only in arithmetic but also in the whole of math Is there a proof for it or is it just assumed?
- 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)
- 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
- 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
- Prove 1 + a + a^2 + a^3 + . . . . a^n-1 = 1-a^n 1-a by mathematical . . .
You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
- Proof that $(AA^{-1}=I) \\Rightarrow (AA^{-1} = A^{-1}A)$
I'm trying to prove a pretty simple problem - commutativity of multiplication of matrix and its inverse But I'm not sure, if my proof is correct, because I'm not very experienced Could you, plea
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