Simplify: (-i)4n + 1, where n is a positive integer.

1.	Simplify: (-i)4n + 1, where n is a positive integer.
Answer» (-i)^{4n + 1} = (i². i)^{4n + 1} = (i³)^{4n + 1} = i^{12n + 3} = i¹²ⁿ. i³ = (i⁴)³ⁿ. i². i = 1. (-1). i = -i. Can be written as (--i)^4n.(-i) =(-i^2)^2n . (-i) =(-1)^2n.(-i) =1. (-i)=-- i

Answer»

(-i)^{4n + 1}

= (i². i)^{4n + 1}

= (i³)^{4n + 1}

= i^{12n + 3}

= i¹²ⁿ. i³

= (i⁴)³ⁿ. i². i

= 1. (-1). i

= -i.

Can be written as (--i)^4n.(-i)

=(-i^2)^2n . (-i)

=(-1)^2n.(-i)

=1. (-i)=-- i

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