Modul kompleksnog broja

Ako je $\vert z\vert=1$ , izračunajte $\vert 1+z\vert^2+\vert 1-z\vert^2$ .

Rješenje. Prema formuli pod (h) iz [M1, zadatak 1.5], vrijedi

$\displaystyle \vert 1+z\vert^2+\vert 1-z\vert^2$	$\displaystyle =(1+z)\overline{(1+z)}+(1-z)\overline{(1-z)}$
	$\displaystyle =(1+z)(1+\overline{z})+(1-z)(1-\overline{z})$
	$\displaystyle =1+\overline{z}+z+z\overline{z}+1-\overline{z}-z+z\overline{z}$
	$\displaystyle =2(1+z\overline{z})=2(1+\vert z\vert^2)=4.$