Complex numbers: show that (a^b)^c has more values than a^(bc)

1. The problem statement, all variables and given/known data



Show that (a^b)^c can have more values than a^(bc)



Use [(-i)^(2+i)]^(2-i) and (-i)^5 to show this.



2. Relevant equations







3. The attempt at a solution



i^i = e^ilni



lni = i ([itex]\pi[/itex] /2 ± k2[itex]\pi[/itex])



so then



i^i = e^(=[itex]\pi[/itex]/2 ±k2[itex]\pi[/itex])



(i^i)^i = e^i([itex]\pi[/itex]/2 ± k2[itex]\pi[/itex])



as e^(±ik2[itex]\pi[/itex]) = 1



you get (i^i)^i = e^i [itex]\pi[/itex]/2



which is one value only (equal to i^-1 which is -i)



this is not what the question suggests



:confused:



please help!