Question

Calculati modulul numarului complex z=2*(1-i)^{3}

Answer 1

z= 2(2-2i)= 4-4i

|z|= rad(4²+4²)= rad32

(1-i)³= (1-i)(1-i)(1-i)= (1-i-i+i²)(1-i)= 2-2i

Answer 2

Răspuns:

$|z|=|2\cdot (1-i)^3| = 2 |1-i|^3.$

Dar $|1-i|=\sqrt{1^2+(-1)^2}=\sqrt{2}$.

Rezulta ca $|z| = 2 (\sqrt{2})^3 = 4 \sqrt{2}.$