limit equals the imaginary number, i

Question

Hello can a limit equal just the imaginary number? and if it does equal the imaginary number, i does the limit exist? I computed a limit of a function which contained z(complex number) and I used L'Hopital's rule and I got the limit, i. So I was wondering whether that meant that the limit exists or not?

Answer 1

Yes, a limit can be equal to an imaginary number.

For example, the constant sequence $\{a_j\}_{j=1}^\infty$ where $a_j=i$ converges to $i$.

If you are working with complex number, a sequence can converge to a complex number.