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Find the value of (3+2i)(i6-i7)(1+i11).

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Question

Find the value of `(3 + 2/i) (i^6 - i^7) (1 + i^11)`.

Sum
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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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Chapter 1: Complex Numbers - Exercise 1.1 [Page 6]

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