Question

Find the least positive integer n foe which `((1+i)/(1-i))^(n)=1`.

Answer 1

Correct Answer - n = 4
`((1+i)/(1-i))=((1+i))/((1-i))xx((1+i))/((1+i))=((1+i)^(2))/((1-i^(2)))=((1+i^(2)+2i))/(2)=(2i)/(2)=i`.
`therefore" "((1+i)/(1-i))^(n)=1 rArr i^(n) = 1 rArr i^(n) = i^(4) rArr n = 4`.