If `|z-1| =1` and arg`(z)=theta`, where `z ne 0` and `theta` is acute, then `(1-2/z)` is equal to

If |z-i|=1 and arg (z) =theta where 0 lt theta lt pi/2 , then cottheta-2/z equals

If |z-i|=1 and arg (z) =theta where 0 lt theta lt pi/2 , then cottheta-2/z equals

If arg(z) = theta , then arg(bar z) =

If arg(z)= theta , then arg( bar z ) = ?

Suppose z is a complex number such that z ne -1, |z| = 1 and arg(z) = theta . Let w = (z(1-bar(z)))/(bar(z)(1+z)) , then Re(w) is equal to

Suppose z is a complex number such that z ne -1, |z| = 1, and arg(z) = theta . Let omega = (z(1-bar(z)))/(bar(z)(1+z)) , then Re (omega) is equal to

If |z^(2)+1|=|z| where arg(z)>0&arg z in[k pi,m pi], then (1)/(k)+(2)/(m) is equal to

If z_(1) and z_(2) are two nonzero complex numbers and theta is a real number, then (1)/(|z_(1)|^(2) + |z_(2)|^(2))[|(cos theta)z_(1) - (sin theta)z_(2)|^(2) + |(sin theta)z_(1) + (cos theta) z_(2)|^(2) ] is equal to ________