This is very simple! Don't be afraid of imaginary numbers guys! If you want to simplify in the form a+bi, like \(\frac{2i+1}{i+3}\), multiply it by the conjugate of the denominator where it is also 1.
So for \(\frac{2i+1}{i+3}\), you multiply it by \(\frac{i-3}{i-3}\), which is the same as 1. This will simplify and won't change the fraction as you are basically multiplying it by 1. Remember to ALWAYS multiply by the conjugate.
This is your method for problems like these