How do you separate out i/i+1?

if you mean i/(i+1) , the answer is;

\(\sqrt{-1}/(\sqrt{-1}+1)\)

now, multiply each side with \((\sqrt{-1}-1)\)

you will get \((-1-\sqrt{-1})/(-1-1)\)

that is \((-1-\sqrt{-1})/-2\)

get rid of the ((-)) ; the answer is most basic this;

\((1+\sqrt{-1})/2\)

\((1+i)/2\)

if you mean (i/i)+1, that is 1+1=2 -_-

1+1=2

i/(i+1)=1/2+i/2

\(\frac{i}{i+1}=\frac {i(i-1)}{(i+1)(i-1)}=\frac {-1-i}{-1-1}=\frac{1+i}{2}=\frac12+\frac 12i\)

as the same as \(a+bi\)

God d**n it Solveit xD, i was really annoyed with your answer and i decided to answer it properly, and after 1 hour of your answer you just posted the answer really xD