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Question
Answer the following:
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")(4 - 3"i") + (5 + 7"i")(4 + 3"i"))/((4 + 3"i")(4 - 3"i"))`
= `((5 + 7"i")(4 - 3"i" + 4 + 3"i"))/(16 - 9"i"^2)`
= `((5 + 7"i")(8))/(16 + 9)` ...[∵ i2 = – 1]
= `(40 + 56"i")/25`
= `40/25 + 56/25"i"`,
which is of the form a + bi.
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