How do you solve 13i/-5-i

i tried multiplying up and bottom by -5-i and got -65i-13i^2/24= -65i+13/24 but thats wrong cause the book said so with no explanation -__-

13i(-5+i)/(-5-i)(-5+i)
-65i-13/25-5i+5i+1
-65i-13/26
-1/2-5i/2

In complex analysis, you have to multiply 13i/-5-i by what is called the complex conjugate. It has the same idea as the difference between two squares.

13i/-5-i(-5+i/-5+i)
-13-65i is your numerator. Remember that i^2=-1
(-5-i)(-5+i)
25-5i+5i+1
26 is your denominator Remember that your answer has to be in the form of a+bi
-13/26-65/26i
-1/2-65/26i is your simplified final answer

you i's cancel out.
then your left with 13/-5