Question

How do you simplify `(3-i)/(4-i)`?

Answer 1

`13/17-1/17i`

Explanation:

Multiply by the complex conjugate of the denominator.

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

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

`(12-i-(-1))/(16-(-1))=(13-i)/17=13/17-1/17i`

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