Limit of exp(z) (complex number)

[rmcclurk]

Homework Statement

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

Homework Equations

See above

The Attempt at a Solution

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

 

[Dick]

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

 

[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?

 

[Dick]

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?

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.

 

[rmcclurk]

Thanks a lot got it figured out