Calculs de distances - Corrigé

Énoncé

Dans le plan complexe, on considère les points \(\text A\) , \(\text B\)  et  \(\text M\) d'affixe respectives 
\(3+4i\)  , \(7+2i\)   et  \(2+3i\) . Calculer \(\text O\text M\) , \(\text A\text B\)  et \(\text M\text A\) .

Solution

\(\text O\text M=\mid2+3i\mid=\sqrt{2^2+3^2}=\sqrt{13}\)

\(\text A\text B=\mid z_A-z_B\mid=\mid3+4i-(7+2i)\mid=\mid-4+2i\mid\) \(=\sqrt{(-4)^2+2^2}=\sqrt{20}=2\sqrt{5}\)

\(\text M\text A=\mid z_M-z_A\mid=\mid 2+3i-(3+4i)\mid=\mid-1+-i\mid = \sqrt{(-1)^2+(-1)^2} = \sqrt{2}\)