State True of False for the following:

If z is a complex number such that z ≠ 0 and Re (z) = 0, then Im (z²) = 0.

State True of False for the following:

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

State True of False for the following:

The locus represented by |z – 1| = |z – i| is a line perpendicular to the join of (1, 0) and (0, 1).

State True of False for the following:

The inequality |z – 4| < |z – 2| represents the region given by x > 3.

State True of False for the following:

Let z₁ and z₂ be two complex numbers such that |z₁ + z₂| = |z₁| + |z₂|, then arg (z₁ – z₂) = 0.