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Question
Answer the following:
Simplify `[1/(1 - 2"i") + 3/(1 + "i")] [(3 + 4"i")/(2 - 4"i")]`
Solution
`[1/(1 - 2"i") + 3/(1 + "i")] [(3 + 4"i")/(2 - 4"i")]`
= `[(1 + "i" + 3 - 6"i")/((1 - 2"i")(1 + "i"))] [(3 + 4"i")/(2 - 4"i")]`
= `[(4 - 5"i")/(1 + "i" - 2"i" - 2"i"^2)] [(3 + 4"i")/(2 - 4"i")]`
= `((4 - 5"i")(3 + 4"i"))/((3 - "i")(2 - 4"i"))`
= `(12 + 16"i" - 15"i" - 20"i"^2)/(6 - 12"i" - 2"i" + 4"i"^2)`
= `(12 + "i" + 20)/(6 - 14"i" - 4)`
= `(32 + "i")/(2 - 14"i")`
= `((32 + "i")(2 + 14"i"))/((2 - 14"i")(2 + 14"i"))`
= `(64 + 448"i" + 2"i" + 14"i"^2)/(4 - 196"i"^2)`
= `(64 + 450"i" - 14)/(4 + 196)`
= `(50 + 450"i")/200`
= `50/200 (1 + 9"i")`
= `1/4 + 9/4"i"`
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