Question

Scrieti sub forma x+yi,cu x,y∈R,numarul (1+i√3)^5.

Answer 1

Poti folosi formula lui Moivre sau binomul lui Newton
(1+i√3)^5=1+5*1*i√3+10*1*(i√3)^2+10*1*(i√3)^3+5*1*(i√3)^4+(i√3)^5=1+5i√3-
-30-30i√3+45+9i√3=16-16i√3

Answer 2

(1+i√3) =2(1/2+i√3/2)=2(cosπ/3+isinπ/3)

(1+i√3) ^5=2^5(cos5π/3+isin5π/3)=32(cos300°+isin300°)=32(1/2-i√3/2)=
=16-16√3 i