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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)`.
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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