Question

sa se calculeze modulul numarului complex x=$[(\sqrt{2} -1)+i( \sqrt{2} +1)] ^{4}$

Answer 1

Avem proprietatea $|z^n|=|z|^n$, deci :$|x|=|[( \sqrt{2}-1)+i( \sqrt{2}+1)]^4|=|( \sqrt{2}-1)+i( \sqrt{2}+1)|^4=$
=$\sqrt{( \sqrt{2}-1)^2+( \sqrt{2}+1)^2}^4= \sqrt{2-2 \sqrt{2}+1+2+2 \sqrt{2}+1 }^4= \sqrt{6}^4=36$