Question

3-2i/1+4i include each step necessary in simplifying

Answer 1

`(3-2i)/(1+4i)=(11)/(17)-(10)/(17)i`

Explanation:

`(3-2i)/(1+4i)` <-- Given

`(3-2i)/(1+4i)*(1-4i)/(1-4i)` <-- Multiply by the conjugate of the denominator as a factor of 1

`((3-2i)(1-4i))/((1+4i)(1-4i))`

`((3)(1)+3(-4i)-2i(1)-2i(4i))/((1)(1)+1(-4i)+4i(1)+4i(-4i))` <-- Use the Distributive Property and FOIL

`(3-12i-2i-8i^2)/(1-4i+4i-16i^2)`

`(3-10i-8i^2)/(1-16i^2)`

`(3-10i-8(-1))/(1-16(-1))` <-- Rewrite
`i^2` as
`-1`

`(3-10i+8)/(1+16)`

`(11-10i)/(17)`

`(11)/(17)-(10)/(17)i` <-- Rewrite in
`a\pm bi` form