Question

Aratati ca numarul a= I$\sqrt{11} -3$ I + $\frac{2}{3- \sqrt{11} }$ este intreg

Va rog din suflet!

Answer 1

a=I√11-3I + 2/(3-√11)=
=√11-3+2(3+√11)/(3-√11)(3+√11)=
=√11-3+2(3+√11)/(3-11)=
=√11-3+2(3+√11)/(-2)=
=√11-3-(3+√11)=
=√11-3-3-√11)=-6

Answer 2

√11=3,...>3, deci I√11-3I=√11-3
√11-3+2(3+√11)/(3-√11)(3+√11)=√11-3+2(3+√11)/(9-11)=
√11-3+2(3+√11)/(-2)=√11-3-3-√11=-6∈Z