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Question
Simplify the following and express in the form a + ib:
`(1 + 2/i)(3 + 4/i)(5 + i)^-1`
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Solution
`(1 + 2/i)(3 + 4/i)(5 + i)^-1`
= `((i + 2))/i*((3i + 4))/i*1/(5 + i)`
= `(3i^2 + 4i + 6i + 8)/(i^2(5 + i)`
= `(-3 + 10i + 8)/(-1(5 + i)` ...[โต i2 = – 1]
= `((5 + 10i))/(-(5 + i))`
= `((5 + 10i)(5 - i))/(-(5 + i)(5 - i)`
= `(25 - 5i + 50i - 10i^2)/(-(25 - i^2)`
= `(25+ 45i -10(-1))/(-[25 -(-1)]`
= `(35 +45i)/(-26)`
= `(-35)/26 - 45/26 i`
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