Question

How do you simplify `9/(7+i)`?

Answer 1

`9/(7+i)=(63-9i)/(50)=63/50-9/50i`

Explanation:

1. Find the complex coniugate of denominator

denominator: `z=7+i`

denominator complex coniugate: `bar(z)=7color(red)-i`

1. Multiply both numerator and denominator for the complex coniugate

`(9)/(7+i)*(7-i)/(7-i)=(63-9i)/(7^2-(i)^2)=`

Remembering that: `i^2=-1`

`=(63-9i)/(49-(-1))=(63-9i)/(49+1)=(63-9i)/(50)=63/50-9/50i`