ExempleCarte 9 sur 120% de la partie

Calculer un module sans développer

#nombres-complexes#module#exemple

$|1+i| = |{-1-i}| = |1+i| = \sqrt2 \qquad\qquad |(1-i)\times(2+3i)| = |1-i|\times|2+3i| = \sqrt2\times\sqrt{13} = \sqrt{26}$

$\left|\frac{1+i}{2}\right| = \frac{|1+i|}{|2|} = \frac{\sqrt2}{2} \qquad\qquad |(1+i)^6| = |1+i|^6 = (\sqrt2)^6 = 8$

$|-i+i| \le |-i|+|i| \iff 0 \le 1+1$

ExempleCarte 9 sur 120% de la partie

#nombres-complexes#module#exemple

$|1+i| = |{-1-i}| = |1+i| = \sqrt2 \qquad\qquad |(1-i)\times(2+3i)| = |1-i|\times|2+3i| = \sqrt2\times\sqrt{13} = \sqrt{26}$

$\left|\frac{1+i}{2}\right| = \frac{|1+i|}{|2|} = \frac{\sqrt2}{2} \qquad\qquad |(1+i)^6| = |1+i|^6 = (\sqrt2)^6 = 8$

$|-i+i| \le |-i|+|i| \iff 0 \le 1+1$