Question Number 19433 by Tinkutara last updated on 11/Aug/17
$$\frac{\sqrt{\mathrm{5}\:+\:\mathrm{12}{i}}\:+\:\sqrt{\mathrm{5}\:−\:\mathrm{12}{i}}}{\:\sqrt{\mathrm{5}\:+\:\mathrm{12}{i}}\:−\:\sqrt{\mathrm{5}\:−\:\mathrm{12}{i}}}\:= \\ $$
Answered by ajfour last updated on 11/Aug/17
$$=\frac{\left(\sqrt{\mathrm{5}+\mathrm{12i}}+\sqrt{\mathrm{5}−\mathrm{12i}}\right)^{\mathrm{2}} }{\mathrm{24i}} \\ $$$$=\frac{\mathrm{10}+\mathrm{2}\sqrt{\mathrm{25}+\mathrm{144}}}{\mathrm{24i}}=\frac{\mathrm{3}}{\mathrm{2i}}=−\frac{\mathrm{3}}{\mathrm{2}}\mathrm{i}\:. \\ $$
Commented by Tinkutara last updated on 11/Aug/17
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much}\:\mathrm{Sir}! \\ $$