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Question
Simplify the following and express in the form a + ib:
`(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")`
Solution
`(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")`
= `(5 + 7"i")[1/(4 + 3"i") + 1/(4 - 3"i")]`
= `(5 + 7"i") [(4 - 3"i" + 4 + 3"i")/((4 + 3"i")(4 - 3"i"))]`
= `(5 + 7"i") [8/(16 - 9"i"^2)]`
= `(5 + 7"i") [8/(16 - 9(-1))]` ...[∵ i2 = – 1]
= `(8(5 + 7"i"))/25`
= `(40 + 56"i")/25`
= `40/25 + 56/25"i"`
= `8/5 + 56/25"i"`.
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