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Question
Answer the following:
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") xx (sqrt(5) + sqrt(3)"i")/(sqrt(5) + sqrt(3)"i")`
= `(sqrt(5) + sqrt(3)"i")^2/((sqrt(5))^2 - (sqrt(3)"i")^2`
= `(5 + 2sqrt(15)"i" + 3"i"^2)/(5 - 3"i"^2)`
= `(5 + 2sqrt(15)"i" - 3)/(5 + 3)` ...[∵ i2 = – 1]
= `(2 + 2sqrt(15)"i")/8`
= `1/4 + sqrt(15)/4"i"`, which is of the form a + bi.
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