Previous Year NEET Question- Complex Numbers

• Q1. If z1, z2, z3 are complex numbers such that |z1| = |z2| = |z3| = |z1+z2+z3|, then |z1-z2| is equal to (a) 0 (b) |z1| (c) |z2| (d) |z3|

Given that |z1| = |z2| = |z3| = |z1+z2+z3|, we can write z1 = r(cosθ + i sinθ), z2 = r(cosφ + i sinφ), z3 = r(cosψ + i sinψ), where r is a positive real number and θ, φ, ψ are real numbers.

We also know that |z1-z2| = |r(cosθ + i sinθ) - r(cosφ + i sinφ)| = |r(cosθ - cosφ) + i r(sinθ - sinφ)|.

Since |cosθ - cosφ| ≤ 1 and |sinθ - sinφ| ≤ 1, we have |z1-z2| ≤ √2