Question Number 158037 by Tawa11 last updated on 30/Oct/21
$$\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\underset{\mathrm{z}\rightarrow−\:\mathrm{i}} {\mathrm{lim}}\:\:\frac{\mathrm{z}\:\:\:−\:\:\:\mathrm{i}}{\mathrm{z}^{\mathrm{2}} \:\:+\:\:\:\mathrm{1}} \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:\:\underset{\mathrm{z}\rightarrow−\:\mathrm{i}} {\mathrm{lim}}\:\:\frac{\mathrm{z}\:\:\:+\:\:\:\mathrm{i}}{\mathrm{z}^{\mathrm{2}} \:\:+\:\:\:\mathrm{1}} \\ $$$$\left(\mathrm{3}\right)\:\:\:\:\:\:\:\:\:\underset{\mathrm{z}\rightarrow\mathrm{i}} {\mathrm{lim}}\:\:\frac{\mathrm{2z}^{\mathrm{2}} \:\:\:−\:\:\:\mathrm{zi}\:\:\:+\:\:\:\mathrm{1}}{\mathrm{z}\:\:−\:\:\mathrm{i}} \\ $$