Question Number 51922 by aseerimad last updated on 01/Jan/19
$${find}\:{the}\:{value}\:{of}... \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\frac{{i}}{\mathrm{1}+\frac{{i}}{\mathrm{1}+{i}}}}} \\ $$$${pls}\:{help}. \\ $$
Answered by ajfour last updated on 01/Jan/19
$$\mathrm{1}+\frac{{i}}{\mathrm{1}+{i}}\:=\:\mathrm{1}+\frac{{i}\left(\mathrm{1}−{i}\right)}{\mathrm{2}}\:=\:\frac{\mathrm{3}+{i}}{\mathrm{2}} \\ $$$$\mathrm{1}+\frac{\mathrm{1}}{\frac{{i}}{\mathrm{1}+\frac{{i}}{\mathrm{1}+{i}}}}\:=\:\mathrm{1}+\frac{\mathrm{3}+{i}}{\mathrm{2}{i}}\:=\:\frac{\mathrm{3}+\mathrm{3}{i}}{\mathrm{2}{i}} \\ $$$$\mathrm{1}−\frac{\mathrm{2}{i}}{\mathrm{3}+\mathrm{3}{i}}\:=\:\frac{\mathrm{3}+{i}}{\mathrm{3}\left(\mathrm{1}+{i}\right)}\:=\:\frac{\left(\mathrm{3}+{i}\right)\left(\mathrm{1}−{i}\right)}{\mathrm{6}} \\ $$$$\:\:=\:\frac{\mathrm{1}−{i}}{\mathrm{3}}\:. \\ $$$$ \\ $$
Commented by aseerimad last updated on 01/Jan/19
Thank you!