# Region of convergence

1. Aug 28, 2005

### EvLer

One more:
after doing Laplace transform for this:

$$f(t) = e^{(7+5j)t}u(t-1)$$

where u(t) = 1 for t >= 0 and 0 otherwise;
so here's what I have:

$$L[f(t)] = \frac {e^{-(s-7-5j)}}{s-7-5j}$$

so, my reasoning was that it would converge if Re > 7 because that's the value for which exponential would converge. But why exactly do we not care about Im? I know that by Euler's formula, it $$e^{jw}$$ would just be oscillating but don't I need a condition for denominator of L[f(t)]?
Thanks for your time and explanation.

Last edited: Aug 28, 2005
2. Aug 28, 2005

### lightgrav

It is bad to have denominator of zero.
Looks like, if Re > 7 strictly (not >=)
the denominator can't be zero.

3. Aug 28, 2005

### EvLer

let's say I have $$L[f(t)] = \frac{1}{s-a}$$