Verified answer

1+i/(1-i)² =

1+i/(1-i)² * [ (1+i)² / (1+i)² ] = [ (1+i)(1+i)² ] / [ (1-i)² * (1+i)² ]

(1-i)² * (1+i)² = [ 1 - i^2 ] ^ 2 = [ 1 - (-1) ] ^ 2 = 2^2 = 4 -------------------->

[ (1+i)(1+i)² ] / [ (1-i)² * (1+i)² ] = [ 1 + i ] ^ 3 / 4

if you make [ 1 + i ] ^ 3 simpler , it changes to (2i - 2)

so, [ 1 + i ] ^ 3 / 4 = ( 2i - 2 ) / 4 = i / 2 - 1 /2