[tex]i^1\cdot i^2\cdot i^3\cdot ...\cdot i^{100}=i^{1+2+3+...+100}=i^{ \frac{100\cdot101}{2}}=i^{50\cdot101}= i^{5050}= \\ =i^{5048+2}=i^{5048}\cdot i^2=1\cdot(-1)=-1[/tex]
Retine:
[tex]i^{4k}=1 \\ i^{4k+1}=i \\ i^{4k+2}=-1 \\ i^{4k+3}=-i[/tex]
pentru orice k numar natural.