W = sinx + icosx and u = cscx + isecx .then | w / u | =

|w| = sqrt( sin ^2 x + cos^2 x) = 1

|u]^2 = csc^2 x + sec^2 x = (1/ sin ^2 x) + (1/ cos^2 x) = ( cos^2 x + sin ^2 x)/ ( sin ^2 x cos ^2 x)
= 1/ ( sin ^2 x cos^2 x)

so |u| = 1/ ( sin x cos x)

so |w/u] = |w|/|u| = sin x cos x