If $A=2+i$, $O=-4$, $P=-i$, and $S=2+4i$, find $A-O+P+S$.
To add complex numbers, I need to add their real and imaginary parts separately. So, for $A-O+P+S$, I need to find the real part and the imaginary part of the sum. The real part is the sum of the real parts of each term: $2-(-4)+0+2=8$. The imaginary part is the sum of the imaginary parts of each term: $1-0-1+4=4$. Therefore, the sum is $8+4i$. 