Voi aplica aceste două proprietăți ale modulului numerelor complexe.
[tex]|z^n| = |z|^n\\ \\ \Big|\dfrac{z_1}{z_2}\Big| = \dfrac{|z_1|}{|z_2|}[/tex]
Aplicându-le vom obtine:
[tex]z = \Big(\dfrac{\sqrt 3 + i}{1+i}\Big)^5 \\ \\ \begin{array}{lcl}|z| &=& \Bigg|\Big(\dfrac{\sqrt 3 + i}{1+i}\Big)^5 \Bigg| = \Bigg|\dfrac{\sqrt 3 + i}{1+i}\Bigg|^5 = \Bigg(\dfrac{|\sqrt 3+i|}{|1+i|}\Bigg)^5 \\\\ &=& \Bigg(\dfrac{\sqrt{({\sqrt 3})^2+1^2}}{\sqrt{1^2+1^2}}\Bigg)^5= \Bigg(\dfrac{\sqrt{4}}{\sqrt 2}\Bigg)^5 = (\sqrt{2})^5 = \\ \\ &=&4\sqrt 2 \end{array}[/tex]
