Question

State True or False for the following:

For any complex number z the minimum value of |z| + |z – 1| is 1.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Let z = x + yi

∴ |z| + |z – 1| = `sqrt(x^2 + y^2) + sqrt((x - 1)^2 + y^2)`

The value of |z| + |z – 1| is minimum, When x = 0, y = 0 i.e., 1.