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Question
Simplify the following and express in the form a + ib:
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`
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Solution
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`
= `((sqrt(5) + sqrt(3)"i")(sqrt(5) + sqrt(3)"i"))/((sqrt(5) - sqrt(3)"i")(sqrt(5) + sqrt(3)"i")`
= `(5 + 2sqrt(15)"i" + 3"i"^2)/(5 - 3"i"^2)`
= `(5 + 2sqrt(15)"i" + 3(-1))/(5 - 3(-1)` ...[∵ i2 = – 1]
= `(2 + 2sqrt(15)"i")/8`
= `(1 + sqrt(15)"i")/4`
= `1/4 + (sqrt(15)"i")/4`.
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