Simplify the complex number. Express your answer in a + bi form and include each step necessary in simplifying.(3-2i)/(1+4i)

Question

Simplify the complex number. Express your answer in a + bi form and include each step necessary in simplifying.
`(3-2i)/(1+4i)`

Answer 1

`(x+iy)/(u+iv)*(u-iv)/(u-iv)=((x+iy)(u-iv))/(u^2-(iv)^2)`

`=(xu-i^2yv+iyu-ixv)/(u^2+v^2)`

`=\underbrace{(xu+yv)/(u^2+v^2)}_a+i\underbrace{(yu-xv)/(u^2+v^2)}_b`