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Question
Find the value of `(3 + 2/"i")("i"^6 - "i"^7)(1 + "i"^11)`
Solution
i6 = (i2)3 = (– 1)3 = – 1
i7 = i6 × i = (i2)3i = (– 1)3i = – i
i11 = i10 × i = (i2)5i = (– 1)5i = – i
`∴(3 + 2/"i")("i"^6 - "i"^7)(1 + "i"^11)`
`= (3 + 2/"i")(-1 - (-"i"))(1 +(-"i"))`
`= (3 + 2/"i")(-1 + "i")(1 - "i")`
= `(3 + 2/"i")(1 - "i")(1 - "i")`
= `(3 + (2"i")/"i"^2)(-1 + "i" + "i" - "i"^2)`
= `(3 + (2"i")/(-1))[-1 + 2"i" - (-1)]`
= (3 - 2i)(2i)
= 3(2i) - 2i(2i)
= 6i - 4i2
= 6i - 4(- 1)
= 6i + 4
= 4 + 6i
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