Is it REAL?

Algebra Level 3

Find the value of i i i^i .

Here, i = 1 i=\sqrt{-1}

.2078795764....... -i+.2078795764.... i+.2078795764.... -i

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3 solutions

Chew-Seong Cheong
Jan 30, 2015

Similar solution as Renz Jimwel Mina , using Euler Identity:

e i θ = cos θ + i sin θ e^{i\theta} = \cos {\theta} + i \sin{\theta}

i i = ( 0 + i ) i = ( cos π 2 + i sin π 2 ) i = ( e i π 2 ) i = e π 2 = 0.207879576 \Rightarrow i^i = (0 + i)^i = (\cos{\frac{\pi}{2}} + i \sin{\frac{\pi}{2}})^i = (e^{i\frac{\pi}{2}})^i = e^{-\frac{\pi}{2}} = 0.207879576

Renz jimwel Mina
Jul 23, 2014

e^iπ=-1 =>e^(iπ/2)=i =>e^((i^2 π)/2)=i^i =>e^((-π)/2)=i^i And so this is it.

i^i = e^(iΠ/2)^i = e^(-Π/2)

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