Question

qual o valor de i^10+i^-100

Answer 1

i^1^0+i^-^1^0^0=i^2+i^0=-1+1=0 

Answer 2

$i=\sqrt1\\i^2=-1\\i^3=-1i\\i^4=1\\i^5=\sqrt1=i\\i^6=-1\\i^7=-1i\\i^8=1\\\vdots\qquad\vdots\\\\\\\\i^{10}+i^{-100}\longrightarrow-1+\dfrac{1}{i^{100}}\longrightarrow-1+\dfrac{1}{1}\longrightarrow-1+1=\boxed{0}$