Limit of exp(z) (complex number)

1. Jul 1, 2009

rmcclurk

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

Find limit as z->infinity of exp(z) where z is complex

2. Relevant equations

See above

3. The attempt at a solution

The solution should be that the limit does not exist, but I don't know why. Any explanations?

2. Jul 1, 2009

Dick

Put z=iy, where y is real. Now let y->infinity.

3. Jul 1, 2009

rmcclurk

Is it because e^iy = r(cos(y)+i*sin(y)) and that equation simply oscillates and never goes to infinity no matter how large y gets?

4. Jul 1, 2009

Dick

Right, if you put r=1. Or consider z=x and z=(-x) for x real and let x->+infinity. One limit is infinity, and the other is zero. There is no definite single limit as z->infinity. Consider definite cases of z->infinity to get a feeling for what's going on.

5. Jul 1, 2009

rmcclurk

Thanks a lot got it figured out