Question Number 1318 by 123456 last updated on 22/Jul/15
$$\eta:\mathbb{C}^{\mathrm{2}} \rightarrow\mathbb{R}_{+} \\ $$$$\eta\left({x},{y}\right)=\mid\mid{x}\mid−\mid{y}\mid\mid \\ $$$$\eta\left({x},{y}\right)=\mathrm{0}\overset{?} {\Leftrightarrow}{x}={y} \\ $$$$\eta\left({x},{y}\right)\overset{?} {=}\eta\left({y},{x}\right) \\ $$$$\eta\left({x},{z}\right)\overset{?} {\leqslant}\eta\left({x},{y}\right)+\eta\left({y},{z}\right) \\ $$$${x}\in\mathbb{C} \\ $$$${y}\in\mathbb{C} \\ $$$${z}\in\mathbb{C} \\ $$
Commented by prakash jain last updated on 22/Jul/15
$$\eta\left({x},{y}\right)=\eta\left({y},{x}\right) \\ $$$${x}=\mathrm{2}+\mathrm{3}{i},\:{y}=\mathrm{2}−\mathrm{3}{i} \\ $$$$\eta\left({x},{y}\right)=\mathrm{0} \\ $$