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Question
Simplify:
`(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^584 (i^8 + i^6 + i^4 + i^2 + 1))/(i^574 (i^8 + i^6 + i^4 + i^2 + 1))`
= `(i^584)/(i^574)`
= i10
= (i2)5
= (–1)5
= – 1
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