Consider z1 = r1(cos θ1 + i sin θ1), z2 = r2(cos θ2 + i sin θ2), where r1, r2 are real numbers, 0 ≤ θ1 ≤ π/2, 0 ≤ θ2 ≤ π/2, and i = √−1. If |z1 + z2| = |z1| + |z2|, which one of the following conditions is necessarily CORRECT?

Question

Accepted Answer

The correct answer is D, θ1 = θ2. GATE 2026 official key: (D). Equality in |z1+z2| = |z1|+|z2| holds only when z1 and z2 point in the same direction, i.e. θ1 = θ2.