Need to solve a sumi/(1-i) + i/(1+i)

To solve i/(1-i) +i/(1+i).

i
is the sqrt (-1). So i^2 = -1.

To simplify the expression,
we  multiply both numerator and denominator by the same expression and also we convert
the denominator into a real number.

The first
term:

i/(1-i) =
i(1+i)/(1-i)(1+i)

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

i/(1-i) =
(i-1)/1+1)

i/(1-i) =
(i-1)/2.......................(1).

The second
term:

i/(1+i) =
i(1-i)/(1+i)(1-i)

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

i/(1+i) =
(i-1)/(1+1)

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

Adding (1) and (2) , we
get:

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

i/(1-i) + i/(1+i)  =
2i/2

i/(1-i) +i/(1+i) = i