NDA Mathematics Question (2026) — Solution

Step-by-step solution

Given 3Z_1 4Z_2 is purely imaginary. Let 3Z_1 4Z_2 = i k, where k R . Z_1 Z_2 = 4 3 i k Let 4 3 k = y, so Z_1 Z_2 = i y, where y R . We need to evaluate | Z_1+Z_2 Z_1-Z_2 |. Dividing the numerator and the denominator by Z_2, we get: | Z_1 Z_2 + 1 Z_1 Z_2 - 1 | Substituting Z_1 Z_2 = i y: | i y + 1 i y - 1 | = |1 + i y| |-1 + i y| Since |1 + i y| = 1^2 + y^2 and |-1 + i y| = (-1)^2 + y^2 = 1 + y^2 , we have: 1 + y^2 1 + y^2 = 1 Answer: 1