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11 there are multiple ways of writing out a given complex number, or a number in general Then prove it by induction. The complex numbers are a field
It's a fundamental formula not only in arithmetic but also in the whole of math This should let you determine a formula like the one you want Is there a proof for it or is it just assumed?
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. 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
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 But i think that group theory was the other force. 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).
注1：【】代表软件中的功能文字 注2：同一台电脑，只需要设置一次，以后都可以直接使用 注3：如果觉得原先设置的格式不是自己想要的，可以继续点击【多级列表】——【定义新多级列表】，找到相应的位置进行修改
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
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
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