What is the value of \[{{\left( -\sqrt{-1} \right)}^{4n+3}}+{{\left( {{i}^{41}}+{{i}^{-257}} \right)}^{9}},\] where \[n\in N\]?

What is the value of \[{{\left( -\sqrt{-1} \right)}^{4n+3}}+{{\left( {

1.	What is the value of \[{{\left( -\sqrt{-1} \right)}^{4n+3}}+{{\left( {{i}^{41}}+{{i}^{-257}} \right)}^{9}},\] where \[n\in N\]?
A.	0
B.	1
C.	i
D.	\[-i\]
Answer» D. \[-i\]

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What is the value of \[{{\left( -\sqrt{-1} \right)}^{4n+3}}+{{\left( {{i}^{41}}+{{i}^{-257}} \right)}^{9}},\] where \[n\in N\]?

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