The value of n(--1)4n-3, where n ∈ N, is ______. - Mathematics

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The value of (- sqrt(-1))^(4"n" - 3), where n ∈ N, is ______.

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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APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 5 Complex Numbers and Quadratic Equations
Solved Examples | Q 16.(iv) | Page 83

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