i raised to the power of i

Remember the general rule

a^b = e^{a \ ln(b)}

Using this rule we can compute i raised to the power of i

i^i = e^{i \ ln(i)} = e^{i i\pi/2} = e^{-\pi/2} = 0.207879576 \cdots

remember that

i=\sqrt{-1}

ln(1)=0

ln(i)=i\frac{\pi}{2}

and i i = \sqrt{-1} \sqrt{-1} = -1

Advertisements

About Suresh Emre

I have worked as a physicist at the Fermi National Accelerator Laboratory and the Superconducting Super Collider Laboratory. I am a volunteer for the Renaissance Universal movement. My main goal is to inspire the reader to engage in Self-discovery and expansion of consciousness.
This entry was posted in mathematics, tutorial and tagged . Bookmark the permalink.