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Question
Prove that `(1 + "i")^4 xx (1 + 1/"i")^4` = 16
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Solution
`(1 + "i")^4 xx (1 + 1/"i")^4`
= `[(1 + "i")(1 + 1/"i")]^4`
= `[(1 + "i") ((1 + "i"))/"i"]^4`
= `[((1 + "i")^2)/"i"]^4`
= `(1 + 2"i" + "i"^2)^4/"i"^4`
= `(1 + 2"i" - 1)^4/1` ...[∵ i2 = – 1]
= 16i4
= 16 ...[∵ i4 = 1]
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