Question

How do you divide `3+i div 1-4i`?

Answer 1

`-3/17+13/17i`

Explanation:

Multiply by the complex conjugate.

`(3+i)/(1-4i)=(3+i)/(1-4i)((1+4i)/(1+4i))=(3+12i+i+4i^2)/(1+4i-4i-16i^2)=(1+13i+4i^2)/(1-16i^2)`

Recall that `i=sqrt(-1)`, so `i^2=-1`.

`=(1+13i+4(-1))/(1-16(-1))=(1-4+13i)/(1+16)=(-3+13i)/17=-3/17+13/17i`

Notice how the answer is written in the `a+bi` form of a complex number.