problem with the exponential function

Question

I have a problem :

$ e^i = e^{i*2\pi*1/(2\pi)} = ({e^{i*2\pi}})^{1/(2\pi)} = 1^{1/(2\pi)} = 1$

and this is obviously not true.
Where did I go wrong?

May be of interest https://math.stackexchange.com/questions/1462146/how-to-calculate-ii — cgiovanardi, Dec 23 '17 at 11:11

score 2 · Accepted Answer · answered Dec 22 '17 at 16:07

2

The property $a^{b/c}= (a^b)^{1/c}$ does not hold for all numbers (not for non-real or negatives. This is because this property defines a composition of functions that in this case cannot be defined.

answered Dec 22 '17 at 16:07

Rebellos

21,324

score 1 · Answer 2 · answered Dec 22 '17 at 16:07

1

You assumed that $a^{bc}=(a^b)^c$. Not true. Actually, it doesn't even make sense in general.

answered Dec 22 '17 at 16:07

José Carlos Santos

427,504

problem with the exponential function

2 Answers2