Two i's

Algebra Level 3

What kind of a number is i i ? i^i?

Note that i = − 1 i = \sqrt -1

Is purely imaginary Is purely real I want the solution

Aman Dubey by Aman Dubey , 22, India

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2 solutions

Aman Dubey
Apr 12, 2016

i = e i π 2 i= e^{i\frac {\pi}{2}}

⇒ i i = e − π 2 \Rightarrow i^i = e^{-\frac {\pi}{2}}

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@Good Solution. Looking through your various problems I found that these are very basic questions. If your level of problem solving is this much low , Please try to improve it. Cause IIT is not easy. Good Luck !!!

Anubhav Tyagi - 4 years, 5 months ago
Goh Choon Aik
Apr 14, 2016

i i = − 1 − 1 2 i i ^{i} = -1^{\frac {-1}{2i}}

= − 1 1 1 2 i = - \frac {1}{1^ {\frac {1}{2i}}}

Recall that 1 to the power of anything always equates to 1.

Therefore it reduces into

− 1 1 -\frac{1}{1}

Which is purely real.

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