SOLUTION: let z be a complex number with arg(z)=theta and |z|=k find the following: i) arg(2z) ii) |z| bar iii) |z^2|/|z| bar iv) arg(z bar * z^2)

i) arg(2z)              =    (same as  arg(z) );

ii) |z| bar             z bar is the conjugate to z;  therefore, |z| bar = |z|  (same as for z);

iii) |z^2|/|z| bar      = |z|

iv) arg(z bar * z^2)    =    ( same as arg(z) ).