=( \frac{1+i}{1-i})^{1987} \\  \\  =( \frac{1-i}{1+i}* \frac{1-i}{1-i} )^{1987} \\  \\ =(  \frac{1-2i+i^2}{1-i^2})^{1987} \\  \\ =( \frac{1-2i-1}{1-[-1]}  )^{1987} \\  \\= ( \frac{-2i}{2})^{1987} \\  \\= (-i)^{1987} \\  \\ =(-1)(i)^{1987} \\  \\ =-1.(i)^3 \\  \\ =-1(-i) \\  \\ =i