How do you simplify #(2+i) / (3+i)#?

1 Answer
Dec 13, 2015

Answer:

Multiply the numerator and denominator by the conjugate of the denominator to find that
#(2+i)/(3+i) = 7/10 + 1/10i#

Explanation:

The conjugate of a complex number #a+bi# is #a-bi#. The product of a complex number and its conjugate is a real number. Using that, we get

#(2+i)/(3+i) = (2+i)/(3+i)*(3-i)/(3-i)#

#= ((2+i)(3-i))/((3+i)(3-i))#

#= (7 + i)/10#

#= 7/10 + 1/10i#