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  4. Find the value of (i4n+1-i4n-1/2) .

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Q. Find the value of $\frac{i^{4n+1}-i^{4n-1}}{2}$ .

Complex Numbers and Quadratic Equations

Solution:

$\frac{i^{4n+1}-i^{4n-1}}{2}$
$=\frac{i^{4n} i-i^{4n}i^{-1}}{2}$
$=\frac{i^{2}-1}{2i}$
$=\frac{-2}{2i}$
$=i$