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Question
Evaluate : `("i"^37 + 1/"i"^67)`
Solution
`"i"^37 + 1/"i"^67`
`= ("i"^104 + 1)/"i"^67`
= `(("i"^2)^52 + 1)/("i"^66 xx "i")`
= `((-1)^52 + 1)/(("i"^2)^33 "i")`
= `(1 + 1)/((-1)^33 "i")`
= `2/(-"i")`
= `(-2)/"i"`
= `(-2)/"i" xx "i"/"i"`
= `(-2"i")/"i"^2`
= 2i ...[∵ i2 = – 1]
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