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Question

Mathematics Question on Complex Numbers and Quadratic Equations

Find the value of i4n+1−i4n−12\frac{i^{4n+1}-i^{4n-1}}{2} .

A

ii

B

2i2i

C

−i-i

D

−2i-2i

Answer

ii

Explanation

Solution

i4n+1−i4n−12\frac{i^{4n+1}-i^{4n-1}}{2} =i4ni−i4ni−12=\frac{i^{4n} i-i^{4n}i^{-1}}{2} =i2−12i=\frac{i^{2}-1}{2i} =−22i=\frac{-2}{2i} =i=i