AP EAMCET202125 Aug 2021Morning ShiftMathematicsComplex NumberActual
Let 1, and ^2 be the cube roots of unity. What is the value of (1- + ⁻¹ )^5-2 (1+ - ⁻¹ )^4= ?
Options
- A-64
- B64
- C-64 ⁻¹
- D64 ⁻¹
Correct answer
C. -64 ⁻¹
Step-by-step solution
We have, aligned & (1- + ⁻¹ )^5-2 (1+ - ⁻¹ )^4 = & (1- + ^2 )^5-2 (1+ - ^2 )^4 [ ⁻¹= ^2 ] = & (-2 )^5-2 (-2 ^2 )^4 [ 1+ + ^2=0 ] aligned aligned & =-32 ^5-32 ^8=-32 ( ^5+ ^8 ) & =-32 ( ^2+ ^2 )=-64 ^2=-64 ⁻¹ aligned