Prove that following inequalities:
(i) `|(z)/(|z|) -1| le |arg z|` (ii) `|z-1|le|z| |arg z | + |z|-1|`

If z=(-1-i) , then arg z =

If |z-(4 + 3i) |=1, then find the complex number z for each of the following cases: (i) |z| is least (ii) |z| is greatest (iii) arg(z) is least (iv) arg(z) is greatest

If |z-(4 + 3i) |=1, then find the complex number z for each of the following cases: (i) |z| is least (ii) |z| is greatest (iii) arg(z) is least (iv) arg(z) is greatest

For any complex number z, prove that: (i) -|z| le R_(e)(z)le|z| (ii) -|z|leI_(m)(z)le|z| .

If arg (bar (z) _ (1)) = arg (z_ (2)) then

If | z_ (1) + z_ (2) | = | z_ (1) -z_ (2) |, then arg z_ (1) -arg z_ (2) =

If |z_(1)+ z_(2)|=|z_(1)|+|z_(2)| , then arg z_(1) - arg z_(2) is

If z, z_1 and z_2 are complex numbers, prove that (i) arg (barz) = - argz (ii) arg (z_1 z_2) = arg (z_1) + arg (z_2)

Let | z_ (1) | = | z_ (2) | and arg (z_ (1)) + arg (z_ (2)) = (pi) / (2) then