complex

Find the minimum value of x² + y² + (x - 1)² + y²
= x² + (x - 1)² + 2y²

And that will be answer to your question.

/a-b/ ≤ /a/ + /b/
use this to get answer as 1
keep it simple

it follows from triangle inequality that "sum of distance of a point P from two points, A and B, is minimum when the point P lies on the line joining A and B and in between them"

(this is quite easy to prove)

|z|+|z-1| is the sum of the distances of the point z in the argand plane from points 0 and 1.

if this has to be minimized then z has to be some point between 0 and 1 on the st line between them.
in that case |z|+|z-1|=1