[tex]\it (1+i)^{8n} = 2^{4n} \ \ \ \ (*)[/tex]
Transformăm membrul din stânga:
[tex]\it (1+i)^{8n} = [(1+i)^2]^{4n} = (1+2i+i^2)^{4n} = (1+2i-1)^{4n} =
\\ \\
= (2i)^{4n} = [(2i)^4]^n = (2^4\cdot i^4)^n = (16\cdot1)^n = 16^n[/tex]
Relaița din enunț devine:
[tex]\it 16^n=2^{4n} \Leftrightarrow 16^n=(2^4)^n \Leftrightarrow 16^n= 16^n \ (A)[/tex]
