$\"\"$

Consider the expression is i⁶.

= (i²)³ (Rewrite the expression in terms of i²)

= (-1)³ (Substitute the imaginary unit value i² = -1)

i⁶ = (-1) (Simplify: (-1)³ = -1) $\"\"$

Consider another expression is i⁷

$\"\"$ (Factor the exponent)

$\"\"$ (From the earlier result) $\"\"$

Consider another expression is i⁸

$\"\"$ (Rewrite the expression in terms of i²)

$\"\"$ (Substitute the imaginary unit value i² = -1)

$\"\"$ (Simplify: $\"\"$ )