AP EAMCET20226 Jul 2022Morning ShiftMathematicsComplex NumberActual
For any real number n R,( x+ x)^n=
Options
- An x- nx
- Bn x+ nx
- C^2 n x+2 nx
- Dn x- nx
Correct answer
B. n x+ nx
Step-by-step solution
aligned & Given ( x+ x)^n & ( x+ x)^n= ( e^ i x +e^ -i x +e^ i x -e^ -i x 2 )^n & = ( 2 e^ i x 2 )^n=e^ i n x & = e^ i n x +e^ i n x 2 = e^ i n x +e^ -i n x 2 + e^ i n x -e^ -i n x 2 & = n x+ n x . aligned