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There are infinitely many possible values for $1^i$, corresponding to different branches of the complex logarithm Then prove it by induction. 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.

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11 there are multiple ways of writing out a given complex number, or a number in general This should let you determine a formula like the one you want The complex numbers are a field

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? 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

注1ļ¼šć€ć€‘ä»£č”Øč½Æä»¶äø­ēš„åŠŸčƒ½ę–‡å­— 注2ļ¼šåŒäø€å°ē”µč„‘ļ¼ŒåŖéœ€č¦č®¾ē½®äø€ę¬”ļ¼Œä»„åŽéƒ½åÆä»„ē›“ęŽ„ä½æē”Ø 注3ļ¼šå¦‚ęžœč§‰å¾—åŽŸå…ˆč®¾ē½®ēš„ę ¼å¼äøę˜Æč‡Ŗå·±ęƒ³č¦ēš„ļ¼ŒåÆä»„ē»§ē»­ē‚¹å‡»ć€å¤šēŗ§åˆ—č”Øć€‘ā€”ā€”ć€å®šä¹‰ę–°å¤šēŗ§åˆ—č”Øć€‘ļ¼Œę‰¾åˆ°ē›øåŗ”ēš„ä½ē½®čæ›č”Œäæ®ę”¹ 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. Is there some general formula?

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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 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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