NDA Mathematics Question (2025) — Solution

Step-by-step solution

Rationalizing the expression inside the bracket: 3 +i 3 -i = ( 3 +i)^2 ( 3 -i)( 3 +i) = 3 + i^2 + 2 3 i 3 - i^2 = 3 - 1 + 2 3 i 3 - (-1) = 2 + 2 3 i 4 = 1 2 + 3 2 i Converting to polar form: 1 2 + 3 2 i = ( 3 ) + i ( 3 ) Using De Moivre's theorem to find the cube: ( ( 3 ) + i ( 3 ) )^3 = (3 3 ) + i (3 3 ) = + i = -1 + 0 = -1 Answer: -1