If `z=costheta+isintheta` then find `(1+z)/(1-z)`

If pi lt theta lt 2pi and z=1+costheta+isintheta , then find the value of |z|.

If zne0and2+costheta+isintheta=3//z then find the value of 2(z+barz)-|z|^(2)

If pi

if |z|=1, then find the value of (1+z)/(1-z) .

if |(2iz_1-z_1-z_2)/(2iz_1-z_1-z_2)|=|(costheta+ isintheta)/(costheta-isintheta)| then prove that z_1/z_2 is purely real.

State true or false: If z= (cos2theta+isin2theta)/(costheta+isintheta) then z is unimodular.

If z_(1) and z_(2) are conjugate to each other then find arg (-z_(1)z_(2)).

Convert Z=1/(costheta-isintheta) in a+ib form