# Solving (e[SUP]i[/SUP])[SUP]i[/SUP]

1. Aug 21, 2011

### Icetray

Hey guys,

I have the following question that I am trying to solve. Would really like to solve it on my own first so I'd appriciate hints first! :D

The problem statement, all variables and given/known data

Solve (ei)i

The attempt at a solution

(ei)i = (cos pi/pi + isin pi/pi)i
= (cos i + isin i) (Euler's Formula)

I'm not sure if I'm even right till this point but this is the furthest that I have managed to come so far. ):

2. Aug 21, 2011

### HallsofIvy

Staff Emeritus
It might be more helpful to note that if $y= (e^i)^i$ then $ln(y)= i ln(e^i)= i^2= -1$. And, of course, $ln(re^{i\theta}= ln(r)+ i(\theta+ 2k\pi)$.

3. Aug 21, 2011

### Icetray

Wouldn't that leave me with ln y = -1 and ln y = ln i?

4. Aug 21, 2011

### Staff: Mentor

(ei)i = ei*i = e-1 = ......

5. Aug 21, 2011

### Icetray

I thought of this but didn't think it would be this simple hahaha. So just the calculator value of e-1? :D

6. Aug 21, 2011

### HallsofIvy

Staff Emeritus