If m , n are respectively the least positive and greatest negative integer values of k such that ( 1-i 1+i )^k=-i , then m-n=

Step-by-step solution

Given ( 1-i 1+i )^k=-i (1-i)^2 2 ^k=-i (-i)^k=-i If k=1 (least positive integer) (-i)^1=-i If k=-3 (greatest negative integer) (-i)⁻³=-i So, m=1 and n=-3 m-n=4 .