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Fill in the Blanks
The value of `(- sqrt(-1))^(4"n" - 3)`, where n ∈ N, is ______.
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Solution
The value of `(- sqrt(-1))^(4"n" - 3)`, where n ∈ N, is –i.
Explanation:
Here `(- sqrt(-1))^(4"n" - 3) = (-i)^(4"n" - 3)`
= `(-i)^(4n) (-i)^-3`
= `1/(-i)^3`
= `1/(-i^3)`
= `1/i`
= `i/i^2`
= –i
Concept: Algebraic Operations of Complex Numbers
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