The question is given as;
[tex]\frac{13}{5-i}[/tex]To write in form of a+bi , is the standard form of complex numbers.In this case,
you are performing division given a complex number
You find the conjugate of the denominator 5-i which is 5 + i
Then multiply the numerator and denominator with the conjugate as;
[tex]\frac{13(5+i)}{(5-i)(5+i)}[/tex]This will give;
[tex]\frac{65+13i}{5(5+i)-i(5+i)}[/tex]Note that
[tex]i^2\text{ = -1}[/tex]so this will be
[tex]\frac{65+13i}{25+5i-5i-1i^2}=\frac{65+13i}{25-1}=\frac{65}{24}+\frac{13i}{24}[/tex]The correct answer choice is D.
