Question Number 9836 by tawakalitu last updated on 06/Jan/17
$$\mathrm{Prove}\:\mathrm{that}. \\ $$$$\mid\mathrm{z}_{\mathrm{1}} \:+\:\mathrm{z}_{\mathrm{2}} \mid\:\leqslant\:\mid\mathrm{z}_{\mathrm{1}} \mid\:\mid\mathrm{z}_{\mathrm{2}} \mid \\ $$
Commented by FilupSmith last updated on 07/Jan/17
$$\mid{z}_{\mathrm{1}} \mid\mid{z}_{\mathrm{2}} \mid\leqslant\mid{z}_{\mathrm{1}} {z}_{\mathrm{2}} \mid\: \\ $$$$\: \\ $$$$\mid{z}_{\mathrm{1}} +{z}_{\mathrm{2}} \mid\leqslant\mid{z}_{\mathrm{1}} {z}_{\mathrm{2}} \mid \\ $$$${z}_{\mathrm{2}} ={z}_{\mathrm{1}} +{n} \\ $$$$\mid{z}_{\mathrm{1}} +{z}_{\mathrm{2}} \mid=\mid\mathrm{2}{z}_{\mathrm{1}} +{n}\mid\leqslant\mid{z}_{\mathrm{1}} {z}_{\mathrm{2}} \mid \\ $$$$\: \\ $$$$\mid\mathrm{2}{z}_{\mathrm{1}} +{n}\mid\leqslant\mid{z}_{\mathrm{1}} {z}_{\mathrm{2}} \mid \\ $$$${working} \\ $$$${thinking} \\ $$
Commented by prakash jain last updated on 08/Jan/17
$$\mathrm{z}_{\mathrm{1}} =\mathrm{1} \\ $$$$\mathrm{z}_{\mathrm{2}} =\mathrm{0} \\ $$$$\mid\mathrm{z}_{\mathrm{1}} +\mathrm{z}_{\mathrm{2}} \mid=\mid\mathrm{1}+\mathrm{0}\mid=\mathrm{1} \\ $$$$\mid\mathrm{z}_{\mathrm{1}} \mid\mid\mathrm{z}_{\mathrm{2}} \mid=\mathrm{0} \\ $$$$\mid\mathrm{z}_{\mathrm{1}} \:+\:\mathrm{z}_{\mathrm{2}} \mid\:\:\nleqslant\:\:\mid\mathrm{z}_{\mathrm{1}} \mid\:\mid\mathrm{z}_{\mathrm{2}} \mid \\ $$
Commented by prakash jain last updated on 08/Jan/17
$$\mathrm{The}\:\mathrm{question}\:\mathrm{should}\:\mathrm{be} \\ $$$$\mid\mathrm{z}_{\mathrm{1}} +\mathrm{z}_{\mathrm{2}} \mid\leqslant\mid\mathrm{z}_{\mathrm{1}} \mid+\mid\mathrm{z}_{\mathrm{2}} \mid \\ $$