AP EAMCET20227 Jul 2022Morning ShiftMathematicsComplex NumberActual
If 1, , ^2 are the cube roots of unity, then (2- )^2 (2- ^2 )^2 (2- ¹⁰ )^2 (2- ¹¹ )^2=
Options
- A-7^4
- B7^4
- C7^8
- D-7^8
Correct answer
B. 7^4
Step-by-step solution
1, , ^2 are the cube roots of units. 1+ + ^2=0 Given, (2- )^2 (2- ^2 )^2 (2- ¹⁰ )^2 (2- ¹¹ )^2 aligned & = (2- ) (2- ^2 ) ^2 (2- ) (2- ^2 ) ^2 & = (2- ) (2- ^2 ) ^4 & = 4-2 ( + ^2 )+ ^3 ^4 & =(4-2(-1)+1)^4=7^4 aligned