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Question
Find the value of `(3 + 2/i) (i^6 - i^7) (1 + i^11)`.
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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)(1 - i)(1 - i)`
= `-(3 + 2/i)(1 - i)^2`
= `-(3 + 2/i)(1 - 2i + i^2)`
= `-(3 + 2/i)(1 - 2i + i^2)` ...[∵ i2 = −1]
= `-(3 + 2/i)(-2i)`
= 6i + 4
= 4 + 6i
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