Answer
$\frac{15}{13}-\frac{3}{13}i$.
Work Step by Step
The given expression is
$=\frac{6}{5+i}$
The conjugate of the denominator is $5-i$.
Multiply the numerator and the denominator by $5-i$.
$=\frac{6}{5+i}\cdot \frac{5-i}{5-i}$
Use the special formula $(A+B)^2=A^2+2AB+B^2$
$=\frac{6(5-i)}{5^2-i^2}$
Use $i^2=-1$.
$=\frac{6(5-i)}{25+1}$
Simplify.
$=\frac{6(5-i)}{26}$
$=\frac{3(5-i)}{13}$
Use the distributive property.
$=\frac{15-3i}{13}$
Rewrite as $a+ib$.
$=\frac{15}{13}-\frac{3}{13}i$.
