Question

if[ 1+i/1-i]^m=1then find the largest negative integral value of m?

Answer 1

(1+i/1-i)^m =1
( (1+i)(1+i)/1-i(1+i) ) ^m=1
(1 +2i +i^2 / 1- i+i - i^2) ^m =1
(2i/ 2)^m =1
(i)^m =1
We know that( i)^ 4= 1 (smallest value of m)
Therefore m =4