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What is the value of i4n+1-i4n-12? - Mathematics

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Sum

What is the value of `(i^(4n + 1) -i^(4n - 1))/2`?

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Solution

i, because `(i^(4n + 1) -i^(4n - 1))/2 = (i^(4n)i - i^(4n)i^-i)/2`

= `(i - 1/i)/2`

= `(i^2 - 1)/(2i)`

= `(-2)/(2i)`

= i

Concept: Algebra of Complex Numbers
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APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 5 Complex Numbers and Quadratic Equations
Solved Examples | Q 19 | Page 87

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