For a complex number $z$, the minimum value of $\left | z \right |+\left | z-\cos\alpha-i\sin\alpha \right |$ is

If $a, b, c, d$ be a form consecutive term of an increasing A.P., then the roots of the equation $\left( {x - a} \right)\left( {x - c} \right) + 2\left( {x - b} \right)\left( {x - d} \right) = 0$

If $z = x+iy$ and $w = \dfrac{(1-iz)}{(z-i)}$, then $|w| = 1$ implies that, in the complex plane

The modulus of $\overline { 6+{ i }^{ 3 } } +\overline { 6+{ i } }+\overline { 6+{ i }^{ 2 } }$ is-