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11 there are multiple ways of writing out a given complex number, or a number in general 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). The complex numbers are a field
How do i convince someone that $1+1=2$ may not necessarily be true But i think that group theory was the other force. I once read that some mathematicians provided a very length proof of $1+1=2$
Can you think of some way to
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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. The theorem that $\binom {n} {k} = \frac {n!} {k Otherwise this would be restricted to $0 <k < n$
A reason that we do define $0!$ to be $1$ is so that we can cover those edge cases with the same formula, instead of having to treat them separately
We treat binomial coefficients like $\binom {5} {6}$ separately already 49 actually 1 was considered a prime number until the beginning of 20th century Unique factorization was a driving force beneath its changing of status, since it's formulation is quickier if 1 is not considered a prime
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