Question

How do you simplify `(2+i )/( 7+5i)`?

Answer 1

`19/74-3/74i`

Explanation:

Multiply by the complex conjugate of the denominator.

`(2+i)/(7+5i)*(7-5i)/(7-5i)=(14-10i+7i-5i^2)/(49-35i+35i-25i^2)=(14-3i-5i^2)/(49-25i^2)`

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

`(14-3i-5(-1))/(49-25(-1))=(19-3i)/74=19/74-3/74i`

Note that the answer is written in the complex form `a+bi`.