(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Compute [tex] i^{i} [/tex]

2. Relevant equations

[tex] z = x + iy [/tex]

[tex] z = r \left( cos\theta + isin\theta \right)[/tex]

3. The attempt at a solution

I tried to manipulate the equations for substitution to no avail. I think that the answer is 1, since this is what my calculator told me, but I haven't got any more ideas to proceed with the substitutions for i. Experimenting with different ideas on a calculator, I noticed that [tex] n^{i} [/tex] , where [tex] n [/tex] is a positive integer, gave a complex number of the form, [tex] a = b + ic [/tex], where [tex] a^{2} = 1 [/tex] always, and where [tex] b [/tex] decreases and [tex] c [/tex] increases as the integer [tex] n [/tex] increases.

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# Homework Help: I^i = ?

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