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I am trying to calculate:

  1. $i^2 \div 3$
  2. $i^i$
  3. $(i+1)^{i-1}$.

For the first one, $i = \frac{1}{2}\cdot e^i\cdot\pi$.

So, $(\frac{1}{2}\cdot e^i\cdot\pi)^2 \div 3$, and I tried this trick for the other two but it is not getting me anywhere.

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    At least i^i was the subject of a recent question (which got the proper answer one can imagine) and maybe more of them.2012-09-15
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    I hope you mean $i = e^{i\pi/2}$. And was (1) supposed to be $i^{2/3}$?2012-09-16
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    for (1) I wanted i^2/3 and can you do the explanation without using cis? Thanks2012-09-16
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    You really wanted $i^2/3$, that is, $(i^2)/3$? Do you know what $i^2$ is?2012-09-16

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