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Question
Answer the following:
Simplify: `("i"^238 + "i"^236 + "i"^234 + "i"^232 + "i"^230)/("i"^228 + "i"^226 + "i"^224 + "i"^222 + "i"^220)`
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Solution
`("i"^238 + "i"^236 + "i"^234 + "i"^232 + "i"^230)/("i"^228 + "i"^226 + "i"^224 + "i"^222 + "i"^220)`
= `("i"^230 ("i"^8 + "i"^6 + "i"^4 + "i"^2 + 1))/("i"^220("i"^8 + "i"^6 + "i"^4 + "i"^2 + 1))`
= i10
= (i2)5
= (– 1)5
= – 1.
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