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

1 Answer
Jan 13, 2016

Answer:

#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#