NDA Mathematics Question (2026) — Solution

Step-by-step solution

Let z_1 = + i and z_2 = + i . From the given conditions: z_1 + z_2 = ( + ) + i( + ) = 0 Squaring both sides: (z_1 + z_2)^2 = 0 z_1^2 + z_2^2 + 2z_1 z_2 = 0 Using De Moivre's theorem, z_1^2 = 2 + i 2 and z_2^2 = 2 + i 2 . The product term is 2z_1 z_2 = 2( ( + ) + i ( + )). Substituting these into the squared equation: ( 2 + 2 + 2 ( + )) + i( 2 + 2 + 2 ( + )) = 0 Equating the real part to zero: 2 + 2 + 2 ( + ) = 0 Answer: 0