If 1, , ² are the cube roots of unity, then ( i + ) ( i + ² ) ( i +w⁴ ) ( i + ⁸ ) is equal io

Step-by-step solution

We have, aligned (1+ ) (1+ ² ) (1+ ⁴ ) (1+ ⁸ ) & =&(1+ ) (1+ ² )(1+ ) (1+ ² ) & [ ⁴= ³ = and ⁸- ( ³ )² ²= ³ ] =& (1+ ) (1+ ² ) )²= (1+ + ²+ ³ )² =& ( ³ )² [ 1+ + ²=0 ] &=(1)²=1 [ ³=1 ] aligned