Question Number 18550 by mondodotto@gmail.com last updated on 24/Jul/17
Commented by mondodotto@gmail.com last updated on 24/Jul/17
Answered by Tinkutara last updated on 24/Jul/17
$$\mid\frac{{p}\:+\:\mathrm{2}{i}}{\mathrm{1}\:−\:\mathrm{2}{i}}\mid\:=\:\mathrm{13} \\ $$$$\Rightarrow\:\mid\frac{\left({p}\:+\:\mathrm{2}{i}\right)\left(\mathrm{1}\:+\:\mathrm{2}{i}\right)}{\mathrm{5}}\mid\:=\:\mathrm{13} \\ $$$$\mid{p}\:+\:\mathrm{2}{pi}\:+\:\mathrm{2}{i}\:−\:\mathrm{4}\mid\:=\:\mathrm{65} \\ $$$$\left({p}\:−\:\mathrm{4}\right)^{\mathrm{2}} \:+\:\mathrm{4}\left({p}\:+\:\mathrm{1}\right)^{\mathrm{2}} \:=\:\mathrm{65}^{\mathrm{2}} \\ $$$${p}^{\mathrm{2}} \:=\:\mathrm{841} \\ $$$${p}\:=\:\pm\:\mathrm{29} \\ $$