solve $\lim_{n \to \infty}\left( \frac{3+2n}{\sqrt{3}+\sqrt{2}n} + i\,n\right)$

Question

I am checking this sequence for convergence but i am not sure whether i am on the right path in calculations, these steps are what i am doing now. $\infty + n$ will go to infinity, right?

$$\lim_{n \to \infty} \frac{3+2n}{\sqrt{3}+\sqrt{2}n} + i\,n = \lim_{n \to \infty} \frac{3+2n}{\sqrt{3}+\sqrt{2}n} + \lim_{n \to \infty}i\,n = \sqrt{2} + \infty = \infty$$

am i okay? can someone please correct me if i am wrong. many thanks for any guidance

Answer 1

If $i$ the imaginary unit then the sequece diverges in modulus.

That sequence will diverge in any case if $i\not = -\sqrt{2}$ is a constant and does not depend on $n$