The power of Imagination

[Silence Resonance]

Two problems...

 

1. What is i to the power i? (hint: it's a real number!)

 

2. Give a good approximation* for i^i^i^... (hint: exponentiation is right-associative. That means x^y^z means x^(y^z), not (x^y^z.)

 

*for grading purposes, I will define a "good approximation" of complex number x to be a number, z, such that |x-z|<0.01

Edited December 5, 2010 by Silence Resonance

[Bignose]

 

 

 

[math]e^{-\frac{\pi}{2}} \approx [/math] 0.20787957635076193 actually any of [math]e^{-\frac{\pi}{2}-2\pi N} [/math] for any integer N is also a valid answer.

 

(0.43828293672163476+0.36059247187510468j)

 

 

 

Edited December 6, 2010 by Bignose

[Silence Resonance]

Right Bignose .. But you did not tell us how u got it ..