If 1, , ² are the cube roots of unity, then (1+ ) (1+ ² ) (1+ ⁴ ) (1+ ⁸ ) is equal to

Step-by-step solution

Given, (1+ ) (1+ ² ) (1+ ⁴ ) (1+ ⁸ ) aligned &=(1+ )(- ) (1+ ³ ) 1+ ( ³ )² ² &=(1+ )(- )(1+ ) (1+ ² ) [ ²=1 ] &=(1+ )² (- - ³ ) &= (1+ ²+2 )(- -1) &=(- +2 ) (+ ² )= ³=1 aligned