we have, i⁵⁷ + i⁷⁰ + i⁹¹ + i¹⁰¹ + i¹⁰⁴

= (i⁴)¹⁴.i + (i⁴)¹⁷.i² + (i⁴)²².i³ + (i⁴)²⁵.i + (i⁴)²⁶

We know that, i⁴ = 1

⇒ (1)¹⁴.i + (1)¹⁷.i² + (1)²².i³ + (1)²⁵.i + (1)²⁶

= i + i² + i³ + i +1

= i -1 -i + i +1

= i