If $${z_1}$$ and $${z_2}$$ are two complex numbers such that $$\,\left| {{z_1}} \right| < 1 < \left| {{z_2}} \right|\,$$ then prove that $$\,\left| {{{1 - {z_1}\overline {{z_2}} } \over {{z_1} - {z_2}}}} \right| < 1$$.

If n^th divisions of the main scale coincide with (n+1)^th divisions of vernier scale. Given one main scale division is equal to 'a' units. Find the least count of the vernier.