If 2 x=-1+ 3 i , then the value of (1-x²+x )⁶- (1-x+x² )⁶ is

Step-by-step solution

Given, 2 x=-1+i 3 x= -1+i 3 2 =w which is one of the cube root of unity. (1-x²+x )⁶- (1-x+x² )⁶ aligned = (1- ²+ )⁶- (1- + ² )⁶ (& . 1+ + ²=0 ) aligned = (- ²- ² )⁶-(- - )⁶= (-2 ² )⁶-(-2 )⁶=2⁶ ¹²- ⁶ =2⁶(1-1) ( ³=1 )=2⁶ 0=0