For any complex number `z` find the minimum value of `|z|+|z-2i|`

For any complex number z, the minimum value of |z|+|z-1|

State true or false for the following. For any complex number z, the minimum value of |z| + |z-1| is 1 .

State ture or false for the following. (i) The order relation is defined on the set of complex numbers. (ii) Multiplication of a non-zero complex number by -i rotates the point about origin through a right angle in the anti-clockwise direction.(iiI) For any complex number z, the minimum value of |z|+|z-1| is 1. (iv) The locus represent by |z-1|= |z-i| is a line perpendicular to the join of the points (1,0) and (0,1) . (v) If z is a complex number such that zne 0" and" Re (z) = 0, then Im (z^(2)) = 0 . (vi) The inequality |z-4|lt |z-2| represents the region given by xgt3. (vii) Let z_(1) "and" z_(2) be two complex numbers such that |z_(1)+z_(2)|= |z_(1)+z_(2)| ,then arg (z_(1)-z_(2))=0 . 2 is not a complex number.

If z is a complex number,then find the minimum value of |z|+|z-1|+|2z-3|

For a complex number z the minimum value of |z|+|z-cos alpha-i sin alpha| (where i=sqrt(-1)) is:

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