Answer 1

`[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"`