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Question
Find the value of `(i^592+ i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`.
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Solution
`(i^592+ i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`
= `(i^10(i^582 + i^580 + i^578 + i^576 + i^574))/(i^582 + i^580 + i^578 + i^576 + i^574)`
= i10
= (i4)2 . i2
= (1)2 (–1)
= –1
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