Răspuns:
Explicație pas cu pas:
z=(√a+i√b)(√a +i^2√b)(√a +i^3√b ).
..(√a+i^4n√b);
i¹=1; i²=-1, i³=i²·i=-1·i=-i; i⁴=(i²)²=(-1)²=1, i⁵=i⁴·i=1·i=i se incep repetarile din 4 in 4
z=(√a+i√b)(√a +i²√b)(√a +i³√b )(√a +i⁴√b )·...·(√a +i⁴ⁿ√b)=
=(√a +i√b )(√a -√b )(√a -i√b)(√a +√b )·...·(√a +i√b )(√a -√b )(√a -i√b)(√a +√b) =((√a +i√b )(√a -i√b ))ⁿ·((√a -√b )(√a +√b ))ⁿ=
=((√a)²-(i√b)²)ⁿ·((√a)²-(√b)²)ⁿ=(a-i²b)ⁿ·(a-b)ⁿ=((a+b)·(a-b))ⁿ=(a²-b²)ⁿ
