Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 66

$5-i$

Multiplying by the conjugate of the denominator, the given expression, $ \dfrac{26}{5+i} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{26}{5+i}\cdot\dfrac{5-i}{5-i} \\\\= \dfrac{26(5)+26(-i)}{(5)^2-(i)^2} \\\\= \dfrac{130-26i}{25-i^2} \\\\= \dfrac{130-26i}{25-(-1)} \\\\= \dfrac{130-26i}{26} \\\\= \dfrac{\cancel{26}(5-i)}{\cancel{26}} \\\\= 5-i .\end{array}