Big Omega of a while loop
Any code that gets executed takes time $\Omega(1)$. That's the most you can say if you don't know anything more about the code. For example, if all your know is that your loop has the form while i &lt; n ..., then it could be that $i = n$, so the loop immediately terminates.

Here are some concrete cases in which we can calculate the complexity:

i = 1
while i &lt; n:
  i = i + 1


This runs in time $\Theta(n)$.

i = 1
while i &lt; n:
  i = i + i


This runs in time $\Theta(\log n)$.

i = 1
j = 1
while i &lt; n:
  i = i + j
  j = j + 1


This runs in time $\Theta(\sqrt{n})$.

See if you can prove all these claims.